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M21Ex1F98 - Math 21 Exam 1 You may not use your calculator...

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Math 21 Exam 1 You may not use your calculator during the first 20 minutes of this exam. Your answers to problem 8 will be collected after 20 minutes. You will then be allowed to use your calculator for the remaining 30 minutes of this exam. 1. (12 points) Let f ( x ) = x 3 + x +1, - 1 x 1. Find the domain and the range of of the inverse function, f - 1 , and sketch the graph of the inverse function on the axes provided. y x 2. (6 points) Suppose that f and g are inverse functions. If f (2) = 3, f (3) = 5, f 0 (2) = 6, f 0 (3) = - 2 / 3, and f 0 (5) = - 10, find g 0 (3). 3. (8 points) Use the properties of logarithms to solve the following equation: ln( x 2 - 2 x ) - ln( x 4 ) = 1 4. (16 points) Evaluate the following limits if they exist. If a limit does not exit, write DNE in the blank provided. Remember to justify your answer. Calculator work alone is not sufficient for full credit.
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