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Solution: 2738. Comparison tests Use the Comparison Test or Limit Comparison Test to

Calculus: Early Transcendentals | 2nd Edition | ISBN: 9780321947345 | Authors: William L. Briggs ISBN: 9780321947345 167

Solution for problem 31 Chapter 8.5

Calculus: Early Transcendentals | 2nd Edition

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Calculus: Early Transcendentals | 2nd Edition | ISBN: 9780321947345 | Authors: William L. Briggs

Calculus: Early Transcendentals | 2nd Edition

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Problem 31

2738. Comparison tests Use the Comparison Test or Limit Comparison Test to determine whether the following series converge. a _ k = 1 1 k3>2 + 1

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Step 1 of 3

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 4 x­>2 x _16 b) lim _2x _ 4 3 2 x­>­ x _ 2x 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 _ x |_ G the inequality |f(x)-L|< H holds. 0 f(x)=2x-2 L=-6 x0 =-2 H =0.02 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 _ 1 7. Find the value of the limit (now you can use L’Hopital’s rule): lim x x xo2 _1 1 8. Find the value of the limit: lim(ln x) xof 1 x 9. Find the value of the limit: lim(1 _ ) 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 2 (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 3 tan x _ c 2 2 ln 2 3 6 3 2 12a) _ x _ 1 x _ b) y= e x _ ln x_1 S 15) 1 ln |1 _ 4ln x | _c 2 13) 17 14) 18 2 8

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Chapter 8.5, Problem 31 is Solved
Step 3 of 3

Textbook: Calculus: Early Transcendentals
Edition: 2
Author: William L. Briggs
ISBN: 9780321947345

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Solution: 2738. Comparison tests Use the Comparison Test or Limit Comparison Test to