Calculus Solutions 18

Calculus Solutions 18 - Answers to Odd-Numbered Problems...

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Unformatted text preview: Answers to Odd-Numbered Problems Section 10.2 Convergence Tests: Positive Series (page 380) 1 ? + f + is smaller than 1 + $ + . 1 2 n 1 8 ~ n = S n- S n- 1 = ~ , S = 1 ; ~ n = 4 , S = ~ ; ~ n = h *- ~ n ~ = ~ n ~ , ~ = h 2 n+l n 1 5 No decision on x b, 7 Diverges: &(I + + . *) 9 x - converges: 5 is larger 11 Converges: 5 is larger 1 5 Diverges: x is smaller 15 Diverges: & is smaller 1 7 Converges: x 8 is larger 19 Converges: C 5 is larger 2 1 L = 0 2 3 L = 0 25 L = 5 2 7 r o 0 t ( v ) ~ + L = $ 29s=l(onlysurvivor) 3 l I f y d e c r e a s e s , ~ ~ y ( i ) ~ ~ ~ y ( x ) d z ~ ~ ; - ' y ( i ) 1 35 x: e-" imO e-ldx = 1; $ + 7 + + . = 55 Converges faster than fi zC- I+ 1 37 Diverges because ST = ln(x2 + 1)Ir = oo 39 Diverges because S r xe-"dx = = oo 4 1 Converges (geometric) because i;(f)'dx < oo 43 (b) J'+' $ > (base 1) (height &) 45 After adding we have 1 + 5 + . . + & (close to ln 2n); thus originally close to ln 2n - In n = In % = ln 2 1000 & 47 Jloo 2 = 2 loo - looo - - .009 49 Comparison test: sin an...
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This document was uploaded on 11/02/2011 for the course MAC 2311 at University of Florida.

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