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06final

# 06final - Math 41 Calculus Final Exam Name Section...

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1. (15 points) Evaluate each of the following limits, showing all reasoning. (a) lim h 0 e 5+2 h - e 5 h (b) lim x 2 + x 2 - 1 x 2 - 5 x + 6
(c) lim x 0 x 0 sin 2 t dt x 0 tan t dt

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2. (15 points) Differentiate, using any method you choose. You do not have to simplify your answers. (a) y = (cos x ) x (b) f ( z ) = e sec 2 z · ln z (c) g ( x ) = sin x 1 ( t 2 + 1) 2006 dt
3. (24 points) Evaluate each of the following integrals, showing all reasoning. (a) 3 2 3 x 2 + 2 x + 1 x dx (b) tan x dx

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(c) 1 - 1 xe x dx (d) x 2 x - 1 dx
(e) arctan x x dx

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4. (8 points) The rate at which the world’s oil is being consumed, measured in billions of barrels
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06final - Math 41 Calculus Final Exam Name Section...

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