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Enter your answers as a comma-separated list. Let’s solve some common problems step-by-step so you can learn to solve them routinely for yourself. In differential calculus basics, you may have learned about differential equations, derivatives, and applications of derivatives. A protein with a mass m disintegrates into amino acids at a rate given by \dfrac {dm}{dt} = \dfrac{-18}{t + 18} in gm/hr. find. Solution for What is the differential form for the total surface area of a frustum of a cone with l as the slant height? A: Consider the following equation of ellipse: x2a2+y2b2=1y2b2=1-x2a2yb=a2-x2a2y=baa2-x2. \frac {dy}{dx} - 5y = e^{3x}, Find a particular solution for the following equation. 2. Consider the polar function r(\theta) = \frac{12}{3 + 2\cos \theta},... Let r(t) = (t^2, 1 - t, 4t). Let C_1 and C_2 be arbitrary constants. Solve the linear equation for y = y(x). Show that for constant A and B y = e^{-3x} (A cos (4x) + B sin (4x)) is a solution to the equation y'' + 6y' + 25y = 0, Find a general solution for the following differential equation. Get help with your Differential calculus homework. asked Jan 29 '19 at 5:35. a. Solve the differential equation y" - y' - 12y = 0 with the initial conditions y(0) = 0, y'(0) = 21. d^2y/dx^2 - 3 dy/dx = 0, Compute the divergence of the vector field. 38. Find the absolute extrema of the function on the closed interval, f(x) = (2/3)x -5 on [-2, 3]. If it is, find a function f such that F = nabla f. F(x, y) = e^x cos y i + e^x sin y j. Find the general solution to the homogeneous differential equation: y" - 8y' + 25y = 0. Tamilnadu Samacheer Kalvi 11th Business Maths Solutions Chapter 5 Differential … Find the differential of the function f(x,y) = xe-y at the point (4,0). f(x) = \frac{x}{1 - \ln(x - 2)}, Find the differential of each function. Therefore, d (x 5 )/dx = 5x 4. y'' + 4 y = 5 e^{-x}. PART 1: MCQ from Number 2 – 100 Answer key: PART 2. This raises several questions. As to his second and third questions, I guess the answer is yes. t^2y'' + 5ty' - 5y = 0. Calculus Trivia Questions & Answers : Math This category is for questions and answers related to Calculus, as asked by users of FunTrivia.com. If it is, solve it. Find the solution to the boundary value problem. question_answer . A comprehensive database of more than 35 calculus quizzes online, test your knowledge with calculus quiz questions. Differential Equations Solve second order, linear, homogeneous ODE / IVP, Solve \frac{dy}{dx}=\frac{cos(x-y)}{sin(x) sin(y)}-1, Solve the following Euler's Equation: t^2 y''(t) + t y'(t) + 9 y(t) = 0, t is greater than 0, Solve the separable differential equation for u. 3\dfrac{d^2y}{dx^2} - 7\dfrac{dy}{dx} + 2y = 0, Solve the differential equation. Solution for 13.Find a differential equation whose general solution is y = c1e2t + c2e−3t. Use Laplace transforms to solve the initial value problem: x'' + 3x' + 2x = t; x(0) = 0, x'(0) = 2. Browse through all study tools. Let . Show more Q&A. 83 5 … Recent questions and answers in Differential Calculus 0 votes. y''-y'-2y=x. A 25 feet ladder is leaning against a building. Find the solution to the initial value problem with a graph of solution y''+y'+2y=0, y(0)=1, y'(0)=0, Solve the following differential equation by a place transforms y''+81y=0 y(0)=0 y'(0)=1. A per... A water trough i 10m long and a cross-section has the shape of an isosceles trapezoid that is 30cm wide at the bottom, 80cm wide at the top, and has a height of 50cm. Solve the following differential equations. y~' - 3y' - 10y = 3e^{-2t}. The top half of the circle lying on the horizontal axis is y = (9 - x^2)^0.5. For each of the following DE's, verify whether the DE is exact. \frac {dy}{dx} + \frac {3y}{x} = x^3 - 2, Solve the differential equation. y’ = 5x 5-1 = 5x 4. The top of the ladder is falling at the rate dy dt = p 2 8 m/min. In this problem you will use undetermined coefficients to solve the nonhomogeneous equation y'' + 2y' + y = 6te-t + 3t + 9 with initial values y(0) = 2 and y'(0) = 1. What is the maximum vertical distance between the line y = x + 56 and the parabola y = x^2 for -7 \le x \le 8? r(t) = \sqrt 2 ti + e^t j + e^{-t} k, \ \ t=0, Solve the following differential equation: 5y'' - 3y = 0, Solve the initial value problem. The radius of a spherical balloon is increasing by 6 cm/sec. In this problem, we will solve the initial value inhomogeneous differential equation in two steps. Give the most general solution, using A and B for any unknown constants, and write y as a real-valued function of x. The deri... Find the particular solution to the following differential equation: y''' + y'' + 3y' -5y = 0. y = Ct^{-3}; ty'(t) + 3y = 0. DIFFERENTIAL FORMS307 39.1. … 3.Let x= x(t) be the hight of the rocket at time tand let y= y(t) be the distance between the rocket and radar station. 6.7 Applications of differential calculus (EMCHH) Optimisation problems (EMCHJ) We have seen that differential calculus can be used to determine the stationary points of functions, in order to sketch their graphs. For the following vector field F, decide whether it is conservative or not by computing curl F. Type in a potential function f (that is, nabla f = F). If initial conditions are given, solve the ODE. h\left( t \right) = {e^{ - 4t}}\left( {{t^2} - {e^{ - t}}} \right), Determine the Laplace Transform for the following function. An object is moving along a straight line so that its acceleration is given by a = 6t^2 - 3t + 4. y''' - 2y'' + y' = e^t \cos t, Find the differential of the function. Online Question and Answer in Differential Calculus (Maxima/Minima and Time Rates) Series. Assume that C is arbitrary constant. Solve for y. The Additional Problems are sometimes more challenging and concern technical details or topics related to the Questions and Problems. Consider the given vector equation. Find a particular solution and the general solution. y^{(4)} + y^{(3)} - 2y'' = 12x + 2. \frac {dy}{dx} + 3y = e^{-2x}, Solve the differential equation. Earn Transferable Credit & Get your Degree, Find the derivative of the function g(x)=\int_{2x}^{3x} \frac{u^2-4}{u^2+4}du g'(x)= [{Blank}], Find the differential of each function. y^{(5)} - 6y''' - y = 0, State whether the following differential equation is homogeneous or nonhomogeneous. If the trough is being filled... Population Growth The population of the world in the year 1650 was about 500 million, and in the year 2010 was 6,756 million. Use MUC (Method of Undetermined Coefficients), ROOM (Reduction of Order Method), or VOP(Variation of Parameter) if necessary. Our online differential calculus trivia quizzes can be adapted to suit your requirements for taking some of the top differential calculus quizzes. The function is subject to the given conditions. Question: Differential Calculus Exercise #3 Application Of Derivatives Solve The Following Problems And Show Your Complete Solution 1. A box with a square base and open top must have a volume of 62,500 cm^3. Find the general solution of the DE: (y^4 -y^4x^2)\ dy = x\ dx. If the bottom of the ladder is pulled along the ground away from the wall at a constant rate of 3 m/s, how fast will the top of the ladder be moving down the... A street light is at the top of a 16 ft pole. Calculus Questions with Answers (3). A water tank is being drained and has the shape of a rectangular box 7m long, 6m wide and 5m high. Y' (O) + Y (O) = 4 Sec Se The General Solution Is Y (0) =. Sign in Register; Differential Calculus (03 62 140) University; University of Windsor; Differential Calculus; Add to My Courses. If the bottom of the ladder slides away from the wall at the rate of 1 m/s, how fast is the angle, between the ladder and the ground, changing when... Find a general solution for the following differential equation. Let F = (2 x y + z^3) i +(x^2) j + (3 x z^2) k. Find the scalar potential from which it derives. A: Critical number occurs if f'=0From the graph we see that f'=0 for x=1,2So x=1,2 are critical numbers... question_answer. f(x, y) = \dfrac {\ln (x + 2y)}{y^2}. If it is conservative, find a function f such that F = f . What are the dimensions of such a rectangle with the greatest possible area? 8 y'' - 6 y' + y = 0. y''' - y' + 2 = 0, State whether the following differential equation is homogeneous or nonhomogeneous. One piece is bent into a square for a frame for a stained glass ornament, while the other piece is bent into a circle for a TV antenna. (Give your answers correct to 2 decimal places.) A company that manufactures bicycles has determined that a new employee can assemble M(d) bicycles per day after d days of on-the-job training where M(d) = (100d^2)/((3d^2)+10)) Find M (5) and int... Find the general solution of the given equation. What are the dimensions of such a rectangle with the greatest possible area? t^2 y'' + 3t y' + 2y = 0, Find the general solution of the given equation. a. Assuming that the population of the w... Find the solution to the following initial value problem: A rectangular plot of farmland will be bounded on one side by a river and on the other three sides by a single-strand electric fence. A patient is injected with a drug and t hours later the concentration of the drug remaining in the patient's bloodstream is given by C(t) in mg/ml. If the top slips down the wall at a rate of 4 ft/s, how fast will the foot be moving away from the wall when the top is 15 feet above the ground? Be sure that math … What is the dimension of such a rectangle with the greatest possible area? answered 1 day ago in Differential Equations by Padma01 (45.2k points) 0 … Two post, one 8 ft. high and the other 12 ft. high, stand 15 ft. apart. The best answers are voted up and rise to the top ... $\begingroup$ There have been several very similar questions to this one in recent years (coming from various user accounts), with an equal insistence that the questioner wants to do diff geom or calculus without mentioning coordinates at all, which is a much stronger requirement than demonstrating "coordinate independence". Use Variation of Parameters to solve the differential equation y'' - 3y' + 2y = -\frac{e^{2x}}{e^x + 1}. What are the dimensions of the rectangle with the maximum area? y = \frac{s}{5 + 2s}. The general solution to the homogeneous differential equation 256x^2y'' + 128xy' + 16y = 0 is the function y(x) = C_1y_1(x) + C_2y_2(x) = C_1 _____ + C_2 ___... Find the general solution to the homogenous differential equation y 8 y + 25 y = 0. Homework Answers; Submit; Sign in; How it works; Examples; Reviews; Homework Answers; Blog; Contact us; Submit. 2. y = {e^x + e^{-x}} / {2}, {d^2 y} / {dx^2} - y = 0. : Lab Instructor: The exam has a total value of 330 points that includes 300 points for the regular exam problems and 30 points for the extra credit problem (Problem number 23). 2 c. 1 d. not... Find the general solution to the homogeneous differential equation: 12y" - 11y' - 5y = 0. science. Get help with your Differential calculus homework. A company estimates that its sales will grow continuously at a rate given by the function S'(t)=17e^t where S'(t) is the rate a which sales are increasing, in dollars per day, on day t a. 0. Questions & Answers on Differential Calculus . THE CALCULUS PAGE PROBLEMS LIST Problems and Solutions Developed by : D. A. Kouba And brought to you by : eCalculus.org Last updated: September 21, 2020 Beginning Differential Calculus : Problems on the limit of a function as x approaches a fixed constant limit of a function as x approaches plus or minus infinity limit of a function using the precise … Verify that x(t) = C_1 \sin(3t) + C_2 \cos(3t) is a solution of the second-order differential equation \dfrac{d^2x}{dt^2} + 9x = 0 for any constants C_1 \text{ and } C_2. (a) y = (Ax + B) e^x (b) y = Acosx+ Bsinx (c) x = (Ay + B) e^y (d) y = Ae^x + \frac{B}{e^x}, Solve the following differential equation: y' = x - y,\\ y(0) = 1 (by substituting u = x - y), Find the general solution of the given differential equation. The length of the box is larger than the width. The fence along three sides is to be made of material that costs $5 per foot, and the material for the fourth side costs $16 pe... 1. 94 352. How fast is the water depth changing when the water depth is 0.9m? What's the difference between early transcendentals and late transcendentals? Following is the list of multiple choice questions in this brand new series: MCQ in Differential Calculus (Maxima/Minima and Time Rates) PART 1: MCQ from Number 1 – 50 Answer key: PART 1. What Height H And Base Radius R Will Maximize The Volume Of The Cylinder? Our online calculus trivia quizzes can be adapted to suit your requirements for taking some of the top calculus quizzes. (B) Find the most general solution to the associated homogeneous differential equation. If it is conservative, determine a potential function. Test your understanding of Differential calculus concepts with Study.com's quick multiple choice quizzes. Background313 40.2. Documents (34)Group; Students . z = e 2 x cos 5 t, Let y = 3x^2 + 5x + 3 . Prev Article Next Article (Last Updated On: January 6, 2021) Below are the answers key for the Multiple Choice Questions in Differential Calculus (Limits and Derivatives) Part 2. Write y as a real-valued function of x. A ladder 5 m long rests against a vertical wall. C(t) = \dfrac{3t}{(t^2 + 36)^\frac{3}{2}} What is... For the following vector field F, decide whether it is conservative or not by computing curl F. Type in a potential function f. If it is not conservative, type N. F(x,y) = -2y i - 1x j, For the following vector field F, decide whether it is conservative or not by computing curl F. Type in a potential function f. If it is not conservative, type N. F(x,y) = (-4x - 5y) i + (-5x + 2y) j. Find a particular solution of y" - 3y' + 2y = -e^x. Find the curl and divergence of the vector field: F(x,y,z) = < \arctan (xy), \arctan (yz), \arctan(zx)>. Find the general solution to the homogeneous second-order differential equation. Drug Reaction The strength of a person's reaction to a certain drug is given by R(Q) = Q(C - Q/3)^1/2 where Q represents the quantity of the drug given to the patient and C is a constant. 2. Help Center Detailed answers to any questions you might have ... Browse other questions tagged calculus ordinary-differential-equations or ask your own question. ... Related Calculus Q&A. {{{d^2}y} \over {d{t^2}}} - 6{{dy} \over {dt}} + 25y = 0, \quad y\left( 0 \right) = 2, \quad y\left( {\pi /8} \right) = 6, Determine the solution to the second order homogeneous initial value differential equation 4y'' + 36y' + 81y = 0,\ y(0) = 8,\ y'(0) = 5,\. Need a fast expert's response? (a) Yes, it is irrotational (b) No, it is rotational, The principal unit normal vector to the curve at the specified value of the parameter. Solve the differential equation. A cylindrical tank of radius 3 feet is being drained of water at a rate of 0.2 ft3/sec. Differential and Integral Calculus Questions and Answers – Differentiation Under Integral Sign « Prev. (a) Find the characteristic polynomial ar^2 + br + c. (b) Find the roots of the auxiliary equation. Let . Solve y" + y = f(x) for f(x) = (sec(x))^3. share | cite | follow | asked 1 min ago. Find A General Solution To The Differential Equation. Questions (44) Publications (9,565) Questions related to Differential Calculus. The general solution of the differential equation 9y" - 3y = 0 can be written in the form where y(x) = Ae^{\lambda_1x} + Be^{\lambda_2x} where \lambda_1 greater than \lambda_2. F = 5y^2 i + (6xy + e^z) j + ye^z k. Determine if the vector field F = \langle \sin x, e^y , z \rangle is conservative, and if so. Write the characteristic equation for the associated homogeneous equation. In this problem you will use variation of parameters to solve the nonhomogeneous equation y'' +4y'+4y=-6e^{-2t} A. Passing the fast paced Higher Maths course significantly increases your career opportunities by helping you gain a place on a college/university course, apprenticeship or even landing a … Continue reading → E-mail *. y'' + y = \tan(x). y'' + y' - 12y = 2te^{-t}, Find a particular solution for the following equation. Find all integers m, such that x^m is a solution of the ODE x^2 y'' - x y' + y = 0. Background307 39.2. A certain instant, the sides are 3 m long and increasing at the rate of 2 m/min. Exercises 309 39.3. Related quizzes can be found here: Calculus Quizzes There are 62 questions on this topic. Let F(x,y) =\sin yi+x\cos yj. Differentiate with respect to using product rule as, Use to obtain, Derivative at is, Plug and to obtain as, Therefore, the derivative of at is . 1) Find a potential function for F or determine that F is not conservative. The consumption of an economy is as follows, where c(x) is the personal consumption expenditure and x is the personal income, both measured in dollars. Exercises 315 40.3. Show that of all the rectangles with a given perimeter the one with the greatest area is a square. z = -4x^2 + 5xy + 8y^2;\\ x = 5, y = -5, dx = 0.03, d y = 0.02.\\ A. t^2 y'' + ty' + y = 0, Find the general solution of the given equation. Calculate the derivative of r(t) . \frac {dy}{dx} - \frac {2y}{x} = x^2 + 5, Solve the differential equation. THE CALCULUS OF DIFFERENTIAL FORMS 305 Chapter 39. MATH 121, Calculus I | Final Exam (Spring 2013) May 15, 2013 | 4:30pm to 7:00pm Name: KU ID No. 9,003 1 1 gold badge 16 16 silver badges 54 54 bronze badges $\endgroup$ add a comment | Active Oldest Votes. Are you working to calculate derivatives in Calculus? Find the particular solution to the following differential equation: y''' - 3y'' + 4y = xe^{2x}. Solve the following differential equation. It … Ship A is sailing south at 35 km/h and ship B is sailing north at 25 km/h. Test your understanding of Differential calculus concepts with Study.com's quick multiple choice quizzes. To reduce storag... Find the total differential. How fast is the radius of the balloon increasing when the radius is 15 cm? D^3(D^2 + 2)^2(D^2 - D - 6)(D - 3)y = 0, Solve following differetial equations. A trough is 10 ft long and its ends have the shape of isosceles triangles that are 2 ft across at the top and have a height of 1 ft. A kite 50 ft above the ground moves horizontally at a speed of 2 ft/s. Answer: y = Your answer should be a function of x. A set of questions on the concepts of the derivative of a function in calculus are presented with their answers. Share a link to this question via email, Twitter, or Facebook. Answers > Math > Calculus. 3 b. Problems 310 39.4. Q: pls help . b. Solve the second-order initial value problem. How do you find the derivative of 3cos(x)? The function y = y(x) satisfies the differential equation \frac{d^2y}{dx^2} + 2\frac{dy}{dx} +5y = 0. y(0) = 5 and y'(0) = 15. Find the general solution of the differential equation. Sign up to join this community. It forms a pile in the shape of a right circular cone whose base diameter and height are always the same. Determine whether or not the vector field is conservative. f'(x) = 9x2; f(0) = -2. To proceed with this booklet you will need to be familiar with the concept of the slope (also called the gradient) of a straight line. Use a differential to estimate the change in y = f(x) = 2x^4 as x changes from 2 to 2.02. MathOverflow is a question and answer site for professional mathematicians. Expert's answer. At what rate is the height of... Find the differential dy. At what rate is the end of the man's shadow moving when he is 12.0 ft from the base of the light? Let f(x)=\sqrt{2x^2+4}, find f'(a). On StuDocu you find all the study guides, past exams and lecture notes for this course. Evaluate \int_{c}e^{y}dx+(xe^{y}+e^{z})dy+ye^{z}dz .C is the curve of intersection of : x^{2}+y^{2}=4 and z=0. All other trademarks and copyrights are the property of their respective owners. Password * t^2 y'' + 3t y' + y = 0, Find the general solution of the given equation. Find the differential dy of the function: y = cos(1 - 2 theta). Find the values of Delta y and dy if x = 4 and Delta x = 0.5. Given that \dfrac{dy}{dx} = \dfrac{2}{x^2} - 3 Find the general solution of the differential equation. Differential Calculus Calculus Differential Equations. 48. Determine the Laplace transform of f(t) = t^2 sin 3t. All rights reserved. Calculus Questions with Answers (4). Find the production level (i.e., the value of x) that will produce the minimum average per unit C(x). g\left( t \right) = 15\sin \left( {6t + {\pi \over 4}} \right), Determine the Laplace Transform for the following function. Problems 310 39.4. How many sets should be made and sold to maximize the weekly profit? A comprehensive database of more than 35 calculus quizzes online, test your knowledge with calculus quiz questions. Use the following initial condition: u(0) = 3. u = \boxed{\space}, Determine the values of ''r'' for which the given differential equation has solutions of the form y=t^{r} for\ t greater then 0. t^{2}{y}''+4t{y}'+2y=0 t^{2}{y}''-4t{y}'+4y=0, Determine the values of ''r'' for which the given differential equation has solutions of the form y = t^r for\ t grater then 0. Help Center Detailed answers to any questions you might have ... Background When first encountering slope fields in calculus or elementary differential equations, students often ask "What is the purpose?" y" + 3y' - 10y = 0; y = 7 and y' = 0 when x = 0, Find the particular solution of the differential equation subject to the given conditions. 6) View Solution. Date Rating. With 1600 m of wire at your disposal, what is the largest area... Find the solution of the differential equations: (a) x dy/dx = y + (x^{2})sinx (b) dy/dx + 3y = 25 sin4x. Consider the function in parametric form { x(t) = 3t cos t, y(t) = 2t sin t. Find d^2 y / dx^2. Use partial derivatives to find a linear fit for a given experimental data. Consider the following. If it is, find a potential function for it. Thus when x(t) = 4 we have that y(t) = 8 p 2 and 4 1 2 +8 2 dy dt = 0. \frac{s}{(s + 1)^{2} + 4}. Verify the function: Is the constant function f(t) = 3 a solution of the differential equation y' = 6 - 2y? vector F = langle y, x, 1 rangle. <12xz^{12} e^{y^{11}}, 11xz^{12} e^{y^{11}}, 12xz^{11} e^{y^{11}}>. Maths or Mathematics TN 11th Std Chapter 9: Differential Calculus Limits and Continuity - Objective type Online Test Questions and Answers with Solution, Explanation, Solved Problems Stack Overflow; For Teams; Advertise With Us; Hire a Developer; … high school math. Step-by-step solutions to all your Calculus homework questions - Slader. Accuracy: A team of editors takes feedback from our visitors to keep trivia as up to date and as accurate as possible. Use it to estimate f(1.05, 1.95). The first three worksheets practise methods for solving first order differential equations which are taught in MATH108. Set up the integral to find the arc length of one leaf of the graph of r = 4 \cos 3\theta. Differential equations 28 Question(s) First Order Equations (Linear And Nonlinear), Higher Order Linear Differential Equations With Constant Coefficients, Euler-Cauchy Equation, Initial And Boundary Value Problems, Laplace Transforms, Solutions of Heat, Wave and Laplace's Equations. Show supporting work. year. ( y ) 3 ln x y = 0. Assume that C,\ C_1 and C_2 are arbitrary constants. Show more Q&A. Find the differential of the function. Find a formula for f^(n) (x). You are planning to make an open rectangular box from a 24-inch by 47-inch piece of cardboard by cutting congruent squares from the corners and folding up the sides. (a). The Questions emphasize qualitative issues and answers for them may vary. Solve \frac{d^2y}{dt^2} + \frac{dy}{dt} - 2y = 8 + 2t - 2t^2 with y(0) = 7,\ y'(0) = 1. Question #154290. if f(1)= 3 and f '(1)=-2 find d/dx [x^2 f(x) ] when x=1. Next » This set of Differential and Integral Calculus Multiple Choice Questions & Answers (MCQs) focuses on “Differentiation Under Integral Sign”. For any given value, the derivative of the function is defined as the rate of change of functions with respect to the given values. Solve the differential equation: x'' + 5x' + 4x = 0. Determine the solution to the second order homogeneous initial value differential equation 12y'' + 46y' + 42y = 0, \quad y(0) = 2, \quad y'(0) = 7. y''' + y'' - y' - y = 0, Determine if the proposed function is a solution to the differential equation. y''-2y'+y= (e^x/x). Find the function __y of x__ such that 10yy' = x \ and \ y(10) = 9 y =. … Solution: Given, y = x 5. Expert's answer . Calculating Derivatives: Problems and Solutions. For y = f(x) = x -x^2,\ x = 3 and \Delta x = 0.02. question_answer. A comprehensive database of differential calculus quizzes online, test your knowledge with differential calculus quiz questions. THE EXTERIOR DIFFERENTIAL OPERATOR313 40.1. Given the second-order homogenous constant-coefficient equation y'' + 6y' + 9y = 0. If so, find a potential function. Calculus questions, on differentiable functions, with detailed solutions are presented. Midterm 8 November 2014, questions and answers … a. y^{(4)}-y=0, \ y(0)=1, \ y'(0)=0, \ y''(0)=1, \ y'''(0)=0. where C is the boundary of the square 0 \leq x \leq 3, 0 \leq y \leq 3 , oriented in the counter clockwise direction. y y 2 y = e 3 x cos 2 x, Determine whether or not the vector field is conservative. \dfrac{d^2y}{dx^2} + 2\dfrac{dy}{dx} = 0, Solve the differential equation. Find the general solution to the following inhomogeneous differential equation. Consider the function y = x^{3/2}. The water is being drained out of the tank at a rate of 25 cm^3/min. Note that we are measuring distance in met... Is the vector field {F}(x,y,z) = 2xyz {i} + (2y + x^2 z {j}) + x^2 y {k} irrotational? If the entire can is to be made out of the same material, find the dimensions (radius and height) of the can... A manufacturer estimates that if x units of a particular commodity are produced, the total cost will be C(x) dollars, where C(x) = x^3 24x^2 + 350x + 338 . Suppose that the cost function for a product is given by C(x) = 0.002x^3 + 8x + 6,244. It turns out to be rather di cult to give a precise description of what a number is, and in this course we won’t try to get anywhere near the bottom of this issue. Find a particular solution and the general solution. 2y'' + y' - 15y = 0, Solve the differential equation. A Guide to Differential Calculus Teaching Approach Calculus forms an integral part of the Mathematics Grade 12 syllabus and its applications in everyday life is widespread and important in every aspect, from being able to determine the maximum expansion and contraction of bridges to determining the maximum volume or maximum area given a function. Find the dimensions of the box that minimize the amount of material used. For the function f(x)=e^{x+y}\ln x, a. find the domain b. find partials f_y and f_{yx}, Create an account to browse all assets today, Differential Calculus Questions and Answers, Biological and Biomedical Access study documents, get answers to your study questions, and connect with real tutors for MATH 1851 : Calculus and ordinary differential equations … Math Calculus Differential Equations. Find the particular solution of the differential equation subject to the given conditions. (If the vector field is not conservative, enter DNE.) Initially the object is at x = 2 and has velocity v = 3. Differentiation is a process where we find the derivative of a function. F\left( s \right) = {\pi \over s} + {{90} \over {{s^4}}} + {{15} \over {{{\left( {s + 4} \right)}^3}}}, Determine the Laplace Transform for the following function. Differentiate with respect to using product rule as, Use to obtain, Derivative at is, Plug and to obtain as, Therefore, the derivative of at is . Find the solution of the differential equation x^2 y'' -5xy' + 5 y = 0. We consider the non-homogenous problem y'' -y' = 1 -2x. f(x) = 6 / x - 2. Q: Find the area enclosed by the ellipse x2/a2 + y2/ b2 = 1 shown in the figure. Test your understanding with practice problems and step-by-step solutions. A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 11 - x^2. … \frac{du}{dt} = e^{2 u + 10 t}. Here is a set of practice problems to accompany the Differentiation Formulas section of the Derivatives chapter of the notes for Paul Dawkins Calculus I course at Lamar University. '' ' - 3y '' + 8ty ' + 2xy = x^4 -,! The cost function for it ( t ) at time t, find f ' ( 0 ) =1 answers. U ) = xe^y ( a ): part ( B ) find a potential function f such that =. People changing after 15 minutes to the following Problems and Show your Complete solution 1 ) compute curl f. 5 } \cosh ( 5x ), where y = 5 e^ { 3x }, \ C_1 C_2... 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