MTH132-Test2 - 3 cm Suppose now its radius is 5 cm(a How...

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Page 1 10/18/2011 Name (Print Clearly): Student Number: Feb 27, 2009 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) 3 2 x y = (b) 2 cos ) 5 2 ( x x y + = (c) x x x x y cos sin cos sin 2 + = (d) ) 1 ( tan 2 5 x y + =
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Page 2 10/18/2011 (e) 1 1 2 + - = x x y (f) 2 2 2 2 ) ( y x y x x - = - (use implicit differentiation) 2 [5 pts each] . Let x x f 5 ) ( = . (a) Find the derivative using the definition. (b) Find the derivative using differentiation rules.
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Page 3 10/18/2011 3 [8 pts] . Show that ) 2 , 1 ( lies on the curve y x y x + = - 2 4 3 3 . Then find an equation for the tangent line to the curve at this point. 4 [10 pts] . A spherical ice ball melts at the rate of min / 10
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Unformatted text preview: 3 cm . Suppose now its radius is 5 cm. (a) How fast is the radius decreasing at this moment? (Hint: 3 3 4 r V π = ) (b) How fast is the surface area of the ice ball decreasing at this moment? (Hint: 2 4 r S ⋅ = ) Page 4 10/18/2011 5. [8 pts] . Let 5 . sin 2 1 ) (-+ + = x x x f (a) Find the linearization of ) ( x f at = x . (b) Estimate ) 1 . ( f using the result of (a). 6. The position of a particle is given by the parametric equations: ) 1 ( 2 , 1 2 2-=-= t t y t x : (a)[4pts] Find dx dy / by using parametric formula. (b)[2pts bonus] Find the values of t for which the curve passes through the origin. (c) [2 pts bonus] Find the corresponding slopes of the tangent lines for the values of t that you found in part (b)....
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MTH132-Test2 - 3 cm Suppose now its radius is 5 cm(a How...

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