sols2 - SOLUTIONS TO HOMEWORK ASSIGNMENT #2 1. Compute the...

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Unformatted text preview: SOLUTIONS TO HOMEWORK ASSIGNMENT #2 1. Compute the following limits: (a) lim x → sin(- x ) sin 3 x (b) lim θ → θ 3 (sin θ ) 2 (c) lim x → √ 1 + 2 x- √ 1- 2 x x (d) lim t → t t + sin t (e) lim z →∞ z 2 + 1 2 z 2- 1 (f) lim x →-∞ cos x x 2 + 1 Solutions: Theses questions use the limit laws (study pages 67-70 and 76) and various algebraic steps. (a) lim x → sin(- x ) sin 3 x =- 1 3 lim x → sin x x 3 x sin 3 x =- 1 3 lim x → sin x x × lim x → 3 x sin 3 x =- 1 3 (b) lim θ → ( θ ) 3 (sin θ ) 2 = lim θ → θ × lim θ → ( θ ) 2 (sin θ ) 2 = 0 × 1 2 = 0 (c) lim x → √ 1 + 2 x- √ 1- 2 x x = lim x → √ 1 + 2 x- √ 1- 2 x x × √ 1 + 2 x + √ 1- 2 x √ 1 + 2 x + √ 1- 2 x = lim x → 1 + 2 x- (1- 2 x ) x ( √ 1 + 2 x + √ 1- 2 x ) = lim x → 2 x x ( √ 1 + x + √ 1- x ) = lim x → 4 √ 1 + 2 x + √ 1- 2 x = 2 by setting x = 0 . The last step uses continuity of the function 4 √ 1 + 2 x + √ 1- 2 x at x = 0....
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This note was uploaded on 01/12/2010 for the course STAT 100 taught by Professor Denissjerve during the Winter '06 term at San Jose State University .

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sols2 - SOLUTIONS TO HOMEWORK ASSIGNMENT #2 1. Compute the...

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