quiz6-sol - AMS 151 (Fall, 2009) Joe Mitchell Applied...

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AMS 151 (Fall, 2009) Joe Mitchell Applied Calculus I Quiz # 6 – Solution Notes 1. (4 points) Compute lim t + 12 te 1 /t - 12 t . We rewrite the expression: lim t + 12 te 1 /t - 12 t = lim t + 12( e 1 /t - 1) 1 /t , and then see that it is of the form 0 0 , so we apply l’Hopital’s rule to get lim t + 12( e 1 /t - 1) 1 /t = lim t + 12( e 1 /t ( - 1 /t 2 )) - 1 /t 2 = lim t + 12 e 1 /t = 12 . 2. (4 points) Compute lim t 0 + 1 t - 1 e t 1 . We rewrite the expression by writing with a common denominator: lim t 0 + 1 t - 1 e t - 1 = lim t 0 + e t - 1 - t t ( e t - 1) , and then see that it is of the form 0 0 , so we apply l’Hopital’s rule to get lim t 0 + e t - 1 - t t ( e t - 1) = lim t 0 + e t - 1 te t + e t - 1 , and see that it is still of the form 0 0 , so we apply l’Hopital’s rule again to get lim t 0 + e t - 1 te t + e t - 1 = lim t 0 + e t te t + e t + e t = 1 2 . 3. (4 points)
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quiz6-sol - AMS 151 (Fall, 2009) Joe Mitchell Applied...

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