MATH 111 Final: MATH 111 Amherst F12M111 2804 29RemyFinal

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turquoisegnu128

15 Feb 2019

School

Amherst College

Department

Mathematics and Statistics

Course

MATH 111

Professor

All

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Document Summary

Final exam math 5, prof. condon, fall 2010. Do all work in the blue books provided. Please clearly show all steps used to obtain your answers. Relax, and good luck: find the equation of the tangent line to the curve y = 5 3x + 1 at the point with x = 0. (you may give the line"s equation in any form. : show that lim x 4. 1 3x = 11, using the formal ( - ) de nition of limits: calculate the following. Simplify your answers. (a) d ds(cid:16) s s2 + 3(cid:17) (b) f (1), for f (x) = (10x 11)6. (c) h 4qx + 1 x + 7i . , on the curve x5y3 + x = y2. x3(cid:17) (e) dy dx (d) lim x 1 (f) lim g(t), for g(t) = t 3 . |2x2 + 6x| has vertical asymptotes: sand is being poured onto the oor at a rate of 2 cubic feet per minute.

Related Questions

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

Solve all please.