# exam1 - (0 0 You choose the free ends(b(5 pts Guess the...

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Exam 1 M170-003 Fall, 2007 Name: (1 pt.) Show all your work. Regardless of your prior experience with calculus, you must use limit methods for all derivatives on this exam. 1. An investment grows according to the formula A ( t ) = 100 e 0 . 1 t where A is measured in dollars and t is measured in years. (a) (5 pts.) Find the average rate of change of A on the interval 0 . 9 t 1 year. (b) (5 pts.) Find the average rate of change of A on the interval 1 t 1 . 1 years. (c) (5 pts.) Guess the instantaneous rate of change of A at time t = 1 year. 1

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2. (15 pts.) If f ( x ) = 2 x - 1, Fnd the rate of change of f at the point x = 5. 2
3. (15 pts.) Use the graph of f shown at right to answer the following questions. x 1 2 1 2 3 f(x) -1 (a) lim x →- 1 + f ( x ) = ? (b) lim x 2 f ( x ) = ? (c) lim x 1 - f ( x ) = ? (d) lim x 1 + f ( x ) = ? (e) lim x 1 f ( x ) = ? 4. Use the graph of f shown at right to: (a) (10 pts.) Compute at least two secant slopes with Fxed end at

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Unformatted text preview: (0 , 0). You choose the free ends. (b) (5 pts.) Guess the tangent slope at (0 , 0). –1 –0.5 0.5 1 –1 –0.5 0.5 1 3 5. (15 pts.) Suppose that y = x + 1 x . Find the slope of the tangent line at the point (1 , 2). 4 6. (15 pts.) A moving object has position (in meters) given by f ( t ) = 30 + 10 t-2 t 2 , with t in seconds. Find its position when its velocity is 8 m/s. 5 7. (10 pts.) You wish to install a cable running from P to Q to R as shown in the Fgure at right. It costs you \$180 per foot for the seg-ment from P to Q and \$100 per foot for the segment from Q to R . Total cost, C , is a func-tion of the distance x from T to Q . Compute the average rate of change of C ( x ) on the interval 0 ≤ x ≤ 50 feet. 350 ft 150 ft x P Q R T 6...
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exam1 - (0 0 You choose the free ends(b(5 pts Guess the...

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