Quiz for MTH 121 - Calc with Analytic Geom I with Bannon at Essex County College (ESSEX)

Quiz Information

 Material Type: Quiz Professor: Bannon Class: MTH 121 - Calc with Analytic Geom I Subject: Mathematics University: Essex County College Term: Summer I 2005 Keywords: Final AnswersYou Have...DifferentiationImplicit DifferentiationMathematics

Sample Document Text

MTH 121 - Summer - 2005 Essex County College - Division of Mathematics Quiz # 51 - Printed May 23, 2005 Name: Signature: Show all work clearly and in order, and box your final answers. Justify your answers algebraically whenever possible. You have 20 minutes to take this 10 point quiz. When you do use your calculator, sketch all relevant graphs and write down all relevant mathematics. 1. Find yprime parenleftbig x2 + y3parenrightbig4 = 2x2y ? 3y2 Solution: Implicit differentiation. parenleftbigx2 + y3parenrightbig4 = 2x2y ? 3y2 4parenleftbigx2 + y3parenrightbig3 · parenleftbig2x + 3y2yprimeparenrightbig = 4xy + 2x2yprime ? 6yyprime 8xparenleftbigx2 + y3parenrightbig3 + 12y2 parenleftbigx2 + y3parenrightbig3 yprime = 4xy + 2x2yprime ? 6yyprime 8xparenleftbigx2 + y3parenrightbig3 ? 4xy = 2x2yprime ? 6yyprime ? 12y2 parenleftbigx2 + y3parenrightbig3 yprime 8xparenleftbigx2 + y3parenrightbig3 ? 4xy = bracketleftBig 2x2 ? 6y ? 12y2 parenleftbigx2 + y3parenrightbig3 bracketrightBig yprime 8xpare...