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# final1 - Name Final A for Calculus I(151K 1 Evaluate the...

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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 .
3. Evaluate the derivative of f ( x ) = 1 2 x + 1 from the definition.

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4. Evaluate the derivative. (a) f ( x ) = ln( x 4 + 1). (b) f ( x ) = sin x x 2 . (c) y = radicalbig ( x 2 + 1)( x + 4) 5 . (d) y = arctan( e x ).
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?
8. Suppose that f ( x ) = 8 x 2 - x 4 . Find the intervals on which f is increasing and de- creasing. Find and classify any critical points. (That is, classify them as local maxima, local minima, or neither.) Determine the intervals of concavity and find any points of inflection. Graph the function.

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9. A box with a square base and an open top is to have a volume of 1 cubic meter. If the
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