Old Final (2002 Sp)

# Old Final (2002 Sp) - FINAL EXAM CALCULUS FOR THE SOCIALAND...

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FINAL EXAM CALCULUS FORTHE SOCIALANDMANAGEMENTSCIENCES Math 52-12 Spring 2002 There are 7 questions in all; together they are worth llO%.Please be clear and precise in your solutions; I recommend that you display all your working. 1. Forthe function y = ,.,~x2 detennine the following: .:. .A + 1 (a) The sign-chartfor y (denotewhichisthex-interceptandwhichis theverticalasymp- tote) (b) The derivative y' (c) The equation of the tangent to the graph of y at x = 1 (d) The sign-chart for y' (denote which is the x-intercept and which is the vertical asymptote) (e) The secondderivative y" (f) The sign-chart for y" (denote which is the x-interceptand which is the vertical asymptote) Clearly show me all the steps of your working. 2. Sketch the graph of any function y = f(x) with the following characteristics: 25% 8 A horizontal asymptote at y = - 2. 8 Exactlytwo verticalasymptotes,at x = 0 and x = 2. 8 Exactlythree stationarypoints,at x = 1, x = 3, and x = 5. 8 Withits second-derivative y" havingthe followingsign-chart: + I - I - I + I - 0 2 4 7 Draw a large and careful diagram.

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Old Final (2002 Sp) - FINAL EXAM CALCULUS FOR THE SOCIALAND...

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