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Unformatted text preview: Math 151, Spring 2009, Review Problems for Exam 2 Your first exam is likely to have problems that do not resemble these review problems. 1. A function y = f ( x ) is defined implicitly by the equation x 2 + 3 xy + y 2 = 5 . (a) Find dy dx in terms of x and y . (b) Find the equation of the tangent line to the curve at the point (1 , 1). (c) Show that no point on the graph of x 2 + 3 xy + y 2 = 5 has a horizontal tangent line. 2. Find the points on the graph of y 2 = x 3 9 x + 1 (Figure 1) where the tangent line is horizontal. 4 2 2 4 6 4 2 2 4 6 Figure 1: Graph of y 2 = x 3 9 x + 1. 3. Differentiate the following functions. (a) tan 1 ( x 2 ) 3 x 2 + 3 (b) x cos( x ) (c) 2 x ln ( sin 1 ( x ) ) (d) log 2 ( cos 1 ( x 2 + 1) ) 4. A rocket travels vertically at a speed of 600 mph. The rocket is tracked through a telescope by an observer located 10 miles from the launching pad. Find the rate at which the angle between the telescope and the ground is increasing 1 min after liftoff....
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This note was uploaded on 01/18/2012 for the course MATH 151 taught by Professor Sc during the Spring '08 term at Rutgers.
 Spring '08
 sc
 Math

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