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# E3Review - Exam 3 Review MAC 2233 This is intended to be a...

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Exam 3 Review – MAC 2233 * This is intended to be a tool to help you review some of the material that could appear on the exam. It is not inclusive of all topics discussed in lecture. 1. Graph f ( x ) = ( x - 1) 1 3 ( x + 2) 2 3 . Note: f 0 ( x ) = x ( x - 1) 2 3 ( x + 2) 1 3 and f 00 ( x ) = - 2 ( x - 1) 5 3 ( x + 2) 4 3 2. The graph of f 0 ( x ) is given. Give a possible sketch of f ( x ) if f is known to be continuous. 3. Find the particular function E ( t ) = Ae - bt (where A and b are constants) with E -intercept 4 and such that E (1) = e . What is E(2) ? 4. Find the asymptotes of the function f ( x ) = 2 x 2 - 8 6 - x - x 2 ; evaluate lim x →- 3 + f ( x ) . 5. Sketch the graph of f ( x ) = ln( x - 4) + 2 . Write its inverse function and evaluate lim x 4 + f ( x ) . 6. Find the domain and asymptotes for each of the following functions: f ( x ) = ln(2 x - x 2 ) g ( x ) = e x 2 e x - 4 h ( x ) = 4 1 + ln( x ) 7. Solve these equations for x : (a) ln(2 x - 5) - ln( x - 2) = 0 (b) 5(12 - 2 x 2 ) = 20 8. If f ( x ) has horizontal tangent lines at x = - 2 , x = 1 , x = 5 , and if f 00 ( x ) has the following signs, find the relative extrema of f ( x ) . 9. On which interval(s) is f ( x ) = ( x 2 + 1) e x concave up? concave down? Find all points of inflec- tion. Sketch the graph.

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