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# ANALYTIC GEOM & CALC MATH 171

Texas A&M

GPA 3.6

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This 1 page Class Notes was uploaded by Vivien Bradtke V on Wednesday October 21, 2015. The Class Notes belongs to MATH 171 at Texas A&M University taught by Staff in Fall. Since its upload, it has received 11 views. For similar materials see /class/226036/math-171-texas-a-m-university in Mathematics (M) at Texas A&M University.

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Date Created: 10/21/15

Siuakumar 1 O CO 4 9 d3 1 00 CD C MATH 171 Example Sheet 9 From an old 151 common exam Find all possible values of the real number for which y 5 satis es the differential equation y y y Find an equation of the tangent to the curve y e that passes through the origin Find an equation ofthe tangent to the curve y 5 that is perpendicular to the line 2x73 8 Find all numbers x such that lnm2 7 2x 7 2 g 0 Let C denote the graph of the function y lnz Suppose Pz07 yo7 0 gt 17 is a point on C Suppose that the tangent to C at P meets the m axis at the point Q and that the normal to C 350 111m 2 at P intersects the m axis at R Show that the area of the triangle PQR is Consider the parametric curve C given by the following equations zt lnt yt te 25gt 0 i Find an equation of the tangent line to the curve at the point 07 5 ii Obtain a Cartesian equation for the curve C7 and use it to verify your answer to Part Let fz e ln m z gt O lfg is the inverse function of 1 nd g e If f is a oneto one7 twice differentiable function with inverse function 97 show that 7 f 9 9 lf gzl339 Suppose f is a differentiable function and u gt 0 for every real number u Find the derivative of the function f f 10g2 90 10g2 f 1 Consider the function fz lnm xm2 1 i Show that the domain of f is 7007 00 ii Show that f is an odd function Recall that a function f is said to be odd if ex em iii What is the range of 1 iv Show that f is a oneto one function on 7007 00

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