2001 Spring - Spring_2001 math125

# 2001 Spring - Spring_2001 math125 - MATH 125 FINAL EXAM...

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MATH 125 -- FINAL EXAM -- SPRING 2001 T. Geisser, C. Lanski, V. Scharaschkin, and H. Skogman (in alphabetical order) 1. (30 points) Differentiate the following functions: a) (1 + e x 2 ) 5 b) x x 1 + c) sin () t t dt x 1 3 1 3 + 2. (30 points) (a) Give the definition of: f '( a ) is the derivative of f at a . (b) State the Mean Value Theorem (including its hypothesis). 3. (30 points) Find: (a) xx d x 0 2 π sin ( ) (b) e e dx x x 1 2 3 + ln ln (c) d x 2 1 + 4. (20 points) Consider the function f ( x ) = || x x if x if x 2 9 3 3 63 - - = defined for all x R . Describe all the x R at which f is continuous. You must justify your answer . 5. (40 points) Let g(x) = x 9 e x . Complete each statement. Work out the answers below. The work itself and reasons for the answers must appear to get any credit. i) g is increasing on the intervals _________________________________________ ii) g is decreasing on the intervals _________________________________________ iii) g has local maxima at ________________________________________________ iv) g has local minima at _________________________________________________

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2001 Spring - Spring_2001 math125 - MATH 125 FINAL EXAM...

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