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M408C - Final Exam Practice

# M408C - Final Exam Practice - Exam 3 am Calculators OK 75...

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Exam 3 am Calculators OK 75 minutes 1)(25 points) Let f ( x ) = ln( x ) /x . a) Find the domain and intercepts b) Find all asymptotes c) Differentiate and simplify. 2)(35 points) Let f ( x ) = x 2 e - x on [0 , 3]. a) Differentiate and Simplify b) Find all critical points c) Use the first derivative test to find all local extremes. d) Find all absolute extremes. 3)(40 points) Integrate: a ) 1 0 x e x 2 dx b ) e x ( e x - e - x ) dx c ) e 1 1 x ln x dx d ) sec 2 x tan 2 x dx

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Exam 3B 10am 1 hour 15 minutes 1)(35 points) Let f ( x ) = x ln( x ). a) Find all asymptotes b) Differentiate and simplify. c) Find all critical points. d) Use the first derivative test to find all local extremes 2)(25 points) Let f ( x ) = xe - x 2 . a) Find all asymptotes b) Differentiate and simplify. 3)(40 points) Integrate: a ) ( e x - e - x ) 2 e - x dx b ) x x - 1 dx c ) e 3 e 2 1 x ln x dx d ) 1 tan x dx
Sample Exam 3 No Calculators π 4 0 sin x cos 3 x dx 3 0 x x + 1 dx

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