Please solve this Using Mathematica and upload the (.nb) file

(a) Solve the differential equation:

Plot multiple solutions of the differential equation with values of constants c -2,-1,0,1,2 in a single graph

(b)

Find the value of y(4)

(c) Plot the numerical solution of the differential equation for 0 ≤ χ ≤ 10:

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nathandavegomesLv1

25 Aug 2021

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Do the following tasks using Mathematica.

(a) Plot the curves in a single graph for -2 ≤ χ ≤ 2and shade the region only. Then find the area of the bounded region using Area [] function

(b) Find the length of the entire curve

Hint: Determine the Domain and Range of the function first.

Do not use the built-in ArcLength [] function.

Please UPLOAD the Mathematica file(.nb).

orangerhinoceros356

1. (45 marks) Short-Answer Questions. Put your answer in the box provided but show your work also. Each question is worth 3 marks, but not all questions are of equal difficulty. Full marks will be given for correct answers placed in the box, but at most 1 mark will be given for incorrect answer. Unless otherwise stated, it is not necessary to simplify your answers in this question. a) Find the equation of the tangent plane to the graph of the function z = f(x,y) = sell at (0,1). Answer b) Evaluate (T, 0) if f(x,y) = sin(ry). Answer c) Graph of a function z = f(x,y) is given by: Which of the following level curves correspondes to this function. Answer d) If f(x,y) = e(3x – 2y), find lim - Math)-f(x,y) e) Find % if f(x, y) = x2 - y3 and 2 = r sin(t), y = r cos(t). Answer f) Evaluate the directional derivative of f(x, y) = !at (1, -1) in the direction of u =(2, 1). Answer 8) Does Simono converge? h) Sketch the direction field of the differential equation = 1-2y. i) Consider the differential equation ay = 15 - 31, y(0) = 0, and use Euler's method with step size 0.1 to estimate y(0.1). Answer j) Knowing that (-3,-3) is a critical point of f(x,y) = 2:3 + y2 – 4.cy -3.0, use the second derivative test to find out whether it is a local minimum, local maximum, or a saddle point. Answer k) Solve the initial value problem, dy dt 642 2y + cos(u) y(1) = . Answer 1) Is ū=(2,2, -1) perpendicular to v = (5,-4, 2)? Answer m) Find the area between the graph of y = 1 + sin(x) and y=1-sin(x) from 0 to 7. Answer n) Determine the lentgh of the curve y = 8/2,0 SIS 3. Evaluate and simplify your answer. Answer o) Express the volume of the solid obtained by rotating the bounded region that lies between curves y = (x-2)2 and y=1,150 $4 about the vertical line 2 = 5. Do not evaluate this integral. Answer

5. Do the following tasks using Mathematica.

(a) Plot the above functions in a single graph for

(b) Find the limits of the integration for the area of the region enclosed by

Hint: Solve the equations to find the intersections.

Please do it with Mathmetica and upload the .nb file or you can share link . I will give a like. Thanks

orangerhinoceros356

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