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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 halflife 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
 MathDep
 Math

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