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# finpracA - Math 41 Fall 2005 Practice Final Exam 1 Evaluate...

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Math 41 Fall 2005 Practice Final Exam 1. Evaluate each of the following limits. If there is an inﬁnite limit, then state whether the limit is or -∞ (a) lim x →∞ (ln x ) 2 x (b) lim t 0 2 te - t (c) lim x 0 + cos x x 2. Diﬀerentiate each of the following functions (a) y = x ( e x ) (b) f ( y ) = e y 2 - 3 sin( πy ) (c) g ( x ) = ± x 2 - 2 e cos t +7 t 2 dt 3. Evaluate each of the following integrals. (a) ± e 1 (ln x ) 2 dx (b) ± 1 - 1 sin x x 2 + 2 dx (c) ± t t - 1 dt (d) ± tan - 1 x dx (e) ± 2 1 x ( x 2 - 1) dx (f) ± 2 s 2 + s s 3 / 2 ds 4. The following table shows the velocity v ( t ) (in m/s) after t seconds of an accelerating car on the entrance ramp to a highway.

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5. Find an equation for the tangent line to the graph of the equation x 2 + 2 y 2 = xe y at the point (1 , 0). 6. Find the absolute maximum and minimum values of f ( x ) = 2 x x 2 + 1 on the interval [ - 2 , 2]. 7. A beacon that makes one revolution every 10 s is located on a ship anchored 4 km from a straight shoreline. How fast is the beam moving along the shoreline when it makes
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finpracA - Math 41 Fall 2005 Practice Final Exam 1 Evaluate...

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