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Math 09B Study Guide for Midterms & Final Exams

by: Avid Notetaker

Math 09B Study Guide for Midterms & Final Exams Math 010A

Marketplace > University of California Riverside > Mathematics (M) > Math 010A > Math 09B Study Guide for Midterms Final Exams
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These notes will help get you that extremely sought after 'A'. Use this guide and your other resources to help boost your odds of passing that final! Good luck studying everyone.
Calculus:Several Variables
Meng Zhu
Study Guide
Math, Calculus, Math 09B, final, study guides, midterms
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This 14 page Study Guide was uploaded by Avid Notetaker on Wednesday April 13, 2016. The Study Guide belongs to Math 010A at University of California Riverside taught by Meng Zhu in Winter 2016. Since its upload, it has received 65 views. For similar materials see Calculus:Several Variables in Mathematics (M) at University of California Riverside.


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Date Created: 04/13/16
Calculus BC Final Prep Study Guide 1. Given the parametrically defined function that represents the movement of a particle  x    4sint , y   5cost  where 0 ≤ t≤ 2π : Find the Cartesian equation Graph the function on the given interval indicating on the graph the direction of movement. Find the velocity vector d) Find the speed of the particle at t= π 4 e) Find the length of the curve from t=   π to t= π  6 4 2 d   y Find dx2 for the function defined parametrically as x=t-sint, y=1-cost Find the value of each limit without using L’Hopital’s Rule: a) lim x  _8 x­>2   x  _    16 b) lim _2x _ 4 x­>­      x  _  x     2 c) lim tan 3x 4x x­>0 tan d) lim sin(1 _ cos(t) ) t ­>0 1 - cos t 4. Answer each question using f(x) on the interval from 0 d x d 5 where 2 f(x)= x for 0 ≤ x ≤1, 3 for x= 1, 2 for 1 < x < 4, x-2 for4 < x ≤ 5 a) lim f (x) _ x­>4 b) lim f (x) _ x­>4 c) lim f (x) x­>4 f(4) What value should be assigned to f(x) to make it continuous at x=4? Give a value for δ < 0 _εx satisfying 0 _| x _ x0|_ G the inequality |f(x)-L|< H holds. f(x)=2x-2 L=-6 x =-2 H =0.02 0 6. Without a calculator, show that the equation x 3 _15 x _1 0 has 3 solutions in the interval [-4,4]. What theorem guarantees the existence of these three solutions? 3 x_ 1 7. Find the value of the limit (now you can use L’Hopital’s rule): lim xo2  _1  1 x 8. Find the value of the limit: lim(ln x) xof 1 9. Find the value of the limit: lim(1 _ )x xof x 3 2 2 ³   x sin   ( x    _1)dx  tan   x sec  xdx  ³ Answers: x  2 y 1a) _ 1  b) graph of an ellipse  c) <4cost, -5sint> d) 41 e) 1.151 2 16 25 _1 3 _1 3 2) 3a) b) c) d) 1 (1 _ cos t) 8 2 4 4a) 2 b) 2 c) 2 d) dne e) 2 5) .01 6) x(-4)=-3, x(0)=1, x(1)=-13, x(4)=5 therefore by the Intermediate Value Theorem there must be one solution in each of the following intervals: (-4,0), (0,1), (1,4). 3 3 7) ln 3 8) 1 9) e 10) 1 ( x _1) _ 1 sin 2(  _1) _ c 11) 1 tan  x _ c 2 2 ln 2 3 6 3 2 12a) _ x _ 1 x _ b) y=   x _ ln x_1 e S 15) 1 ln |1 _ 4ln   x | _c 2 13) 17 14) 18 2 8


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