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# ER1 - 4 4 3 4 3 x x x x f-= f 1 2 3 4 2 3-= t t t t t s g e...

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Math 102 Review for Exam #1 Exam Coverage: Sections 11.1-11.4, 12.1-12.5 Date: Wednesday, February 8, 8 am Rooms Sections Main Auditorium 001, 002, 003, 005, 006, 008, 009, 010, 018, 022, 023, 025 Nesbitt 111 004, 011, 013, 017 Nesbitt 125 019, 020 CAT 61 012, 021, 024 1. Let ( 29 2 2 3 2 1 3 2 x x f x x x + - = + + . Find a) 1 lim ( ) x f x →- b) 2 lim ( ) x f x c) x x f ) ( lim 2. Determine the values of x for which the following function is discontinuous. For each, identify which condition for continuity is not satisfied. - < - = 2 , 4 2 1 , 0 1 , 1 ) ( x if x x if x if x x f 3. Determine where 4 3 4 ) ( 2 - + + = x x x x f is continuous. 4. Determine where ( 29 4 f x x = - is continuous 5. Use the definition of the derivative to find ) ( x f for the following functions: a) 12 9 7 ) ( 2 + - - = x x x f b) x x f 1 ) ( = 6. For the function ( 29 2 3 8 2 f x x x = - - + find a. the instantaneous rate of change at x = -2 b. the average rate of change from x =1 to x =4 c. the slope of the tangent line at x = -3 d. values of x where the tangent line is horizontal.

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7. Find the following derivatives: a. 4 3 2 5 ) ( - + - = x x x x f b. 3 3 5 - = x y c. ( 29 3 2 8 5 ) ( - + = x x x f d. 2 2 3 ) 1 ( 5 ) ( - = x x x f e.
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Unformatted text preview: 4 4 3 ) ( 4 3 x x x x f-+-= f. ) 1 2 )( 3 4 ( 2 ) ( 3 +--= t t t t t s g. e e x y x ln ) 2 ln( 5 3 2 + + + =-h. ) 5 ln( + = x e y x 8. Find the equation of the line tangent to the graph of f(x) at x = 2. 3 2 3 ) ( 2 + +-= x x x f 9. Find the value(s) of x where the tangent line is horizontal for ) 45 )( 3 ( ) ( 2-+ = x x x f . 10. Suppose the position of an object moving in a straight line is given by the function , 6 3 5 ) ( 2 + + = t t t s where s represents distance in meters, and t is time in seconds. a. Find average velocity from t=1 to t=5. b. Find instantaneous velocity at t=4. 11. The total sales S (in thousands of CDs) for a compact disk are given by 2 2 90 ( ) 50 t S t t = + where t is the number of months since the release of the CD. a. Find S’(t) b. Find S(10) and S’(10). Write a brief verbal interpretation of the results....
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ER1 - 4 4 3 4 3 x x x x f-= f 1 2 3 4 2 3-= t t t t t s g e...

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