Midterm one - Midterm 1 SOLUTIONS MAT 131 Fall 2011 1 For each of the following limits and one-sided limits determine if it exists If the limit

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Unformatted text preview: Midterm 1 SOLUTIONS MAT 131 Fall 2011 1. For each of the following limits and one-sided limits, determine if it exists. If the limit exists, find it. If it does not exist, determine if it is + ∞ ,-∞ , or neither. (a) lim x → 3 x 2- 6 x + 9 x- 3 = lim x → 3 ( x- 3) 2 x- 3 = lim x → 3 ( x- 3) = 0 (b) lim t →∞ t + 1 t 2 + 1 = 0 because the degree of the denominator is greater than that of the numerator (c) lim x → 2 x 2- 2 x- 2 does not exist , approaches + ∞ from the right and-∞ from the left (d) lim x →∞ 2 x 2- 3 x 4 x 2 + 5 x- 6 = 2 4 = 1 2 because the degree of the numerator and the denominator are equal (e) lim x → + e x 1- e x =-∞ because the denominator → 0 but remains negative, while the numerator is always positive and → 1 (the limit does not exist, but answering “-∞ ” is sufficient) (f) lim t → 1 ( t- 1)cos t = (1- 1)cos1 = 0 , the function is continuous (g) lim t → √ t + 1- 1 t = lim t → √ t + 1- 1 t · √ t + 1 + 1 √ t + 1 + 1 = lim t → t + 1- 1 t ( √ t + 1 + 1) = lim...
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This note was uploaded on 01/13/2012 for the course MAT 131 taught by Professor Christopherbay during the Fall '08 term at SUNY Stony Brook.

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Midterm one - Midterm 1 SOLUTIONS MAT 131 Fall 2011 1 For each of the following limits and one-sided limits determine if it exists If the limit

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