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Unformatted text preview: Midterm 1 SOLUTIONS MAT 131 Fall 2011 1. For each of the following limits and onesided 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.
 Fall '08
 CHRISTOPHERBAY
 Calculus, Limits

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