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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 .
 Winter '06
 denissjerve

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