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Unformatted text preview: 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) = x3 + 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 (2) = 6, f (3) = −2/3, and f (5) = −10, ﬁnd g (3). x 3. (8 points) Use the properties of logarithms to solve the following equation: ln(x2 − 2x) − ln( ) = 1 4 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. 3ex − e−x a) lim x x→∞ e + 2e−x ex − 1 − x b) lim x→0 x2 c) lim arctan(ln x) +
x→0 5. (8 points) Evaluate √ ex dx 1 − e2x 1 6. (12 points) Twenty years ago you obtained a certain amount of a radioactive substance. You observe that currently you have one hundred grams of this substance left. You also know that the half-life of this substance is sixty years. How much of this substance did you have twenty years ago; how much at time t? 7. (14 points) Evaluate the following integrals: a) e3x + 2 dx ex
3π/4 π/2 b) 3 cos x dx sin x 8. (24 points) Find the derivatives of the following functions. Do not simplify your answers. a) e2x+1 e x2 b) x2 tan−1 (x2) √ 1 − 2x c) log5 d) xsin x 2 ...
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This note was uploaded on 01/24/2011 for the course MATH 21 taught by Professor Mathdep during the Winter '98 term at Missouri S&T.
- Winter '98