MAT-1110 Final: MATH 1110 App State summer2017 Final Exam answer key
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Name: answer key: (24 points) all answers should either be , , a ( nite) real number, or dne ( does not exist ). (a) use the graph of the function to. [note: points are out of 200] no calculators. The dashed line indicates that there is a vertical asymptote at x = 1. lim x 1+ f (x) = lim x 1 lim x 2 f (x) = 3 (whereas f (2) = 6) (b) lim x 1 x3 + x2 5x + 3. After plugging in x = 1, we get 0. 0 (an indeterminant form) so we try to apply l"hopital"s rule. After di erentiating the numerator and denominator, we again plug in x = 1 and get 0. After applying l"hopital again, we get (6x + 2)/2 which yields a limit of 4. Since this limit exists, the two applications of l"hopital"s rule are valid and our original limit is 4.
