sols1 - SOLUTIONS TO HOMEWORK ASSIGNMENT #1 1. Compute the...

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Unformatted text preview: SOLUTIONS TO HOMEWORK ASSIGNMENT #1 1. Compute the following limits: (a) lim x →- 2 ( x 3- 3 x 2 + 5) (b) lim x →- 1 (3 x 2 + 2 x + 1) 10 ( x 3 + 5) 5 (c) lim t → 2 (- 3 t 3- 4 t + 5) 1 / 3 (d) lim t → 3 t 2- 9 t- 3 (e) lim t →- 3 t 3- 9 t t + 3 (f) lim z → 9 3- √ z 9- z SOLUTIONS: (a) lim x →- 2 ( x 3- 3 x 2 + 5) = (- 2) 3- 3(- 2) 2 + 5 =- 15 by substituting x =- 2 and using continuity of the polynomial x 3- 3 x 2 + 5 at x =- 2. (b) lim x →- 1 (3 x 2 + 2 x + 1) 10 ( x 3 + 5) 5 = (3(- 1) 2 + 2(- 1) + 1) 10 ((- 1) 3 + 5) 5 = 2 10 4 5 = 1 by substituting x =- 1 and using continuity of the function (3 x 2 + 2 x + 1) 10 ( x 3 + 5) 5 at x =- 1. (c) lim t → 2 (- 3 t 3- 4 t + 5) 1 / 3 = (- 3(2) 3- 4(2) + 5) 1 / 3 = (- 27) 1 / 3 =- 3 by substituting t = 2 and using continuity of the function (- 3 t 3- 4 t + 5) 1 / 3 at t = 2. (d) lim t → 3 t 2- 9 t- 3 = lim t → 3 ( t- 3)( t + 3) t- 3 = lim t → 3 ( t + 3) = 6. Notice that we can not put t = 3 right away as it leads to the nonsense...
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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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sols1 - SOLUTIONS TO HOMEWORK ASSIGNMENT #1 1. Compute the...

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