MATH 126 Final: MATH 126 UW Final Exam Winter 07 Solutions

12 views1 pages

turquoisegnu128

31 Jan 2019

School

Department

Mathematics

Course

MATH 126

Professor

All

For unlimited access to Study Guides, a Grade+ subscription is required.

Document Summary

25 x (b) hint: taylor"s inequality states that the error is bounded by. , which is largest on i when x = 2. upper bound for |f (x)|. So, we can take m to be 2. |5 x|3 (c) hint: show that f (k)(x) = k! Then solve the system 0. 04 < (5 x)k+1 and that the error is bounded by. 2. (a) hint: substitute 2x2 into the taylor series for cos x and subtract. 1 x and 3x into the taylor series for. 32k (2k)! (cid:19) x2k (b) hint: the taylor series for cos x converges for all x, but the taylor series for. 1 x converges only for x such that |x| < 1. This means that the taylor series for f (x) converges only for x such that |2x2| < 1. 8 x4 (c) answer: t4(x) = 5 (b) hint: zzr. Answer: x +px2 + y2 da = z /2.

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

Asap

MATH 126 Final: MATH 126 UW Final Exam Winter 07 Solutions

Document Summary

Get access

Related textbook solutions

Calculus

Single Variable Calculus: Early Transcendentals

CALCULUS:EARLY TRANSCENDENTALS

Related Documents

MATH 126 Final: MATH 126 UW Final Exam Spring 07 Solutions

MATH 126 Final: MATH 126 UW Final Exam aut07 Solutions

MATH 126 Final: MATH 126 UW Final Exam Winter 07

Related Questions