MTH132-Test2

# MTH132-Test2 - a height m 10 and a base radius of m 4...

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Page 1 10/18/2011 Name (Print Clearly): Student Number: Oct 10, 2008 Instructor: Dr. W. Wu Instructions: Answer the following questions in the space provided. There is more than adequate space provided to answer each question. The total time allowed for this quiz is 50 minutes. 1 [5 pts each] . Find dx dy / of each of the following functions. Do Not Simplify (a) x y - = 3 (b) 4 ) 3 4 ( + = x y (c) 1 ) cot (csc - + = x x y (d) x x x x y 3 5 cos 3 sin 1 - = -

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Page 2 10/18/2011 (e) 1 1 2 2 + + + = x x x y (f) x y xy x 2 3 4 3 / 4 3 = - + (use implicit differentiation) 2 [5 pts each] . Let 1 2 1 ) ( + = x x f . (a) Find the derivative using the definition. (b) Find the derivative using differentiation rules.
Page 3 10/18/2011 3 [10 pts] . Show that ) 1 , 1 ( - lies on the curve y x y y x + = + 2 3 3 . Then find an equation for the tangent line to the curve at this point. 4 [10 pts] . Water drains from a conical tank at the rate of min / 5 3 m . The tank stands point down and has

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Unformatted text preview: a height m 10 and a base radius of m 4 . Suppose the water is m 6 deep at this moment. (a) What is the relation between radius of the surface and the depth of the water? (b) What is the relation between the volume and depth of the water? (c) How fast is the water level dropping at this moment? Page 4 10/18/2011 5. [10 pts] . Let 5 . sin 1 ) (-+ + = x x x f (a) Find the linearization of ) ( x f at = x . (b) Estimate ) 1 . ( f using the result of (a). 6. [4 pts bonus]. When a tanker collides with a boat, π 100 3 m of oil is spilled in the ocean. The resulting oil slick forms a right circular cylinder on the surface of the water. If the thickness of the slick is decreasing at a rate of sec / 001 . m , how fast is the radius increasing when the slick is m 01 . thick?...
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## This note was uploaded on 10/17/2011 for the course MTH 133 taught by Professor Staff during the Fall '08 term at Michigan State University.

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MTH132-Test2 - a height m 10 and a base radius of m 4...

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