# 2063 - MATH 201 Final Examination Fall 2009 Instructions No...

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MATH 201 Final Examination Fall 2009 Instructions: No calculators or electronic devices may be used during the exam. You must show work justifying all answers. Answer each question in the space provided. If you need extra space please use the back of each sheet. PART 1 (70 points) Answer all questions 1) (16 points) Find dy dx . Simplify your answers in a) and b). a) b) ( 2 3 421 yxx =+ ) 2 8 x y x = + c) d) 22 sin 2 yx x y += x ( ) 23 tan 2 = + 2) (16 points) Compute each of the following integrals a) 2 32 44 1 xx dx x −+ b) sin cos x xdx c) 3 4 3 1 x dx x + d) 0 4 4s e c( ) x xd x π 3) (10 points) a) State the definition of as a limit. () fx b) Using the definition of the derivative, compute ( ) f x if ( ) 2 2 f xx x = + (No credit will be given for any other method) c) For the function in 3b) using the answer to b) find an equation of the tangent line to at the point . yf x = (1, 3) 4) (8 points) Evaluate the area of the region bounded by the graphs of the equations below. Include a sketch of the region.

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## This note was uploaded on 10/29/2011 for the course MATH Math taught by Professor Ocken during the Spring '11 term at CUNY City.

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2063 - MATH 201 Final Examination Fall 2009 Instructions No...

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