MATH-0042 Study Guide - Final Guide: Farad, Trigonometric Substitution, Constant Function

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turquoisegnu128

9 Jan 2019

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Solutions to math 42 final exam march 17, 2014: (10 points) let t be the triangular region in the xy-plane with vertices (0, 0), (2, 0), and (1, 1). To nd the equation for the line l1, note that the slope is 1 0. 1 0 = 1, and l1 passes through the origin. Hence the equation is y = x; to nd the equation for the line l1, note that the slope is 1 0. 1 2 = 1, and l2 passes through (2, 0). From the picture, we know r = 2 y, dr = dy, y ranges from 0 to 1, and h = xright xleft. From the equations of l1 and l2, we nd xleft = y and xright = 2 y. From the picture, we know dh = dx, rout = 2, and rin = 2 y.

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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

Use the point-slope form linear equation given to complete problems 5-18

y-3=3(x+1)

5. What is the slope of the given line?

6. What point does this line pass through, which is the basis of this equation?

7. Rewrite this equation in the slope-intercept form.

8. What is the y-intercept of this line?

9. Rewrite this equation in standard form.

10. What is the x-intercept of this line?

11. What is the equation in the standard form of a perpendicular line that passes through (5,-1)?

12. What is the x-intercept of the perpendicular line?

13. What is the equation in the standard form of a parallel line that passes through (0,-3)

14. On the parallel line, find the ordered pair where x=2

15. Graph the original equation given include your 3 points from problems 6,8, and 10, labeled A, B, and C respectively

16. Add the perpendicular line to your graph. Include the point given in problem 11 and your point from problem 12, labeled L and M, respectively.

17. Add the parallel line to your graph. Include the point given in problem 13 and your point from problem 14, labeled L and M, respectively.

18. Describe the relationship (if any) between the line drawn in problems 16 and 17.

cerisebeaver906

just number 49 and 51 and can you explain the process

MATH-0042 Study Guide - Final Guide: Farad, Trigonometric Substitution, Constant Function

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