final1 - Name: Final A for Calculus I (151K) 1. Evaluate...

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Name: Final A for Calculus I (151K) 1. Evaluate the limit. (a) lim x 5 - x x 2 - 25 . (b) lim x 8 + x 2 - 100 x - 8 . (c) lim x →∞ 1 + 2 x + x 3 2 + 3 x + 4 x 3 .
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2. Evaluate the limit. (a) lim x 4 x 2 - 16 x - 2 . (b) lim x 1 x + 3 - 2 x 2 - 1 . (c) lim x 0 + (1 + x ) 1 x .
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3. Evaluate the derivative of f ( x ) = 1 2 x + 1 from the deFnition.
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4. Evaluate the derivative. (a) f ( x ) = ln( x 4 + 1). (b) f ( x ) = sin x x 2 . (c) y = r ( x 2 + 1)( x + 4) 5 . (d) y = arctan( e x ).
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5. Find the equation for the tangent line to the curve x 4 + x 2 y + y 2 = 7 at the point ( - 1 , 2). 6. Find the maximum and minimum values of the given function on the given interval: f ( x ) = x x 2 + 1 ; [ - 2 , 2] .
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7. A 6-foot-tall man jogs away from a lightpost at the rate of 12 feet per second. If the lightpost is 20 feet tall, how quickly is the tip of the man’s shadow moving across the ground?
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8. Suppose that f ( x ) = 8 x 2 - x 4 . Find the intervals on which f is increasing and de-
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This note was uploaded on 10/20/2011 for the course MTH 151 taught by Professor Skillings during the Spring '08 term at Miami University.

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final1 - Name: Final A for Calculus I (151K) 1. Evaluate...

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