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# PT2 - x 3 5a Find the absolute max and min of f x = x 5-x 4...

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Practice test for exam #2 in MA135 In addition to problems on this sheet, students should study webwork problems, assigned homework, worked examples in the text, review problems at the end of each chapter, and Prof Sims’ and Greenﬁeld’s sample exams on the web. 1a. Let f ( x ) = e - x 2 +3 . Find f 0 ( x ). 1b. Let f (3) = 1 , g (2) = 3 , f 0 (3) = 4 , g 0 (2) = 5 . If h ( x ) = f ( g ( x )), ﬁnd h 0 (2). 2a. Find the equation of the tangent line to the graph of x 3 + y 3 = y + 21 at (3 , - 2) 2b. If y = x ( x 2 ) , ﬁnd dy dx 3a. The leaning ladder problem from quiz #7. 3b. One end of a rope is fastened to a boat and the other end is wound around a windlass located on a dock at a point 4 m above the level of the boat. If the boat is drifting away from the dock at the rate of 2 m/min, how fast is the rope unwinding at the instant when the length of the rope is 5 m? 4a. Use diﬀerentials to approximate 103. 4b. Find d ( x 2 sin

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Unformatted text preview: x 3 ). 5a. Find the absolute max and min of f ( x ) = x 5-x 4 on [-1 , 1]. 5b. Find the absolute max and min of f ( x ) = ( 9-4 x if x < 1-x 2 + 6 x if x ≥ 1 on [0, 4]. 6. If f ( x ) = 1 √ x , ﬁnd the c in the Mean Value Theorem if a = 1 and b = 4. 7. An eﬃciency study of the morning shift at a factory indicates that the number of units produced by an average worker t hours after 8:00 AM is modeled by the formula Q ( t ) =-t 3 + 9 t 2 + 12 t. At what time in the morning is the worker performing most eﬃciently? 2 8a. Sketch the graph of g ( u ) = u 4 + 6 u 3-24 u 2 + 26. 8b. Sketch the graph of f ( x ) = 3 x-5 x-2 . 8c. Find lim x →∞ ± 1 + 1 2 x ² 3 x . 8d. Find lim x → + ± 2 cos x sin 2 x-1 x ² . 9. Evaluate lim x → 1-cos x sec x ....
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PT2 - x 3 5a Find the absolute max and min of f x = x 5-x 4...

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