Math 156 Test 2A Answer 3 questions Put your name and which 3 questions you want graded at the top of your worksheet. Some of the problems need with(plots) and with(student) or with(Student[Calculus1]) -- Don't forget you need to call these libraries EACH TIME you restart!! JSFH 1a. Graph the curves 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 and g(x) = 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. Use your judgement and trial and error to choose the range. 1 b. Find the intersection points of f(x) and g(x) . 1 c. T Find the area of the region between these curves. 1 d. Graph the volume of the solid of revolution formed by rotating the region in part c about the x-axis. 1 d. Find the volume of the solid of revolution formed by rotating the region in part c about the x-axis. 2a. Graph the curve given by the implicit equation 2*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 in the domain x=-5..5, y=-5..5. Use the scaling option to get a good picture 2b. Find the length of the arc of the upper curve between x=0 and x=4. Hint: Use maple to perform the integration. Note you will get an elliptic function. Find its floating point value. 3a. Graph the function 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 3b. Find the equation of the tangent line to f(x) at x=0 3c. Find the quadratic and cubic approximating Taylor polynomials of f(x) 3c. Graph f(x), its tangent line and the quadratic and cubic approximating polynomials on the same set of axes between -1 and 1. 3d. Use a loop to find the error of the cubic taylor polynomial approximation at the 5 points x=1, x=1/2, x=1/4, x=1/8 and x=1/16 4a. Use Maple to find the partial fraction expansion of 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 4b. Use Maple to integrate the partial fraction 4c. Use Maple to find the integral 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 directly. 4d. How do your answers compare? 4e. Perform 2 integrations by parts and one direct integration to compute the integral 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. Check your answer with direct integration. JSFH