150webfnl-056-1

# 150webfnl-056-1 - Math 150 Final Exam Fall 2005[25 1 Find...

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Math 150 Final Exam Fall 2005 [25] 1. Find the following limits. You must show all your work. a) 1 6 7 3 2 lim 2 2 + + + x x x x x d) 4 3 5 lim 4 + x x x b) x x x 5 sin 2 lim 0 e) h h h 1 4 tan lim 0 + π c) 8 6 12 lim 2 2 4 + x x x x x [10] 2. Use the definition of the derivative to find ) ( x f where 1 1 ) ( = x x f . [30] 3. Find dx dy for the following functions. You do not need to simplify your answer. a) x x x x y cosh sin 1 3 2 + = d) x x x x y + + = 3 2 5 3 b) )) 3 2 ))(tan( 1 (ln( 2 + + = x x y e) x x y sin = c) ) ( cos 3 x e x y + = f) 4 3 1 t dt y x + = [5] 4. Let ) ( x y be defined implicitly by 4 2 2 = + y e y x x . Find dx dy . [10] 5. Determine an equation of the tangent line to the curve of x e x f 2 ) ( = at the point where the curve crosses the line 1 = y . [10] 6. A ladder 15 ft. long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a speed of 2 ft/min, how fast is the ladder sliding down the wall when the base of the ladder is 9 feet from the wall?

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Math 150
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150webfnl-056-1 - Math 150 Final Exam Fall 2005[25 1 Find...

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