MAT 125 Lecture Notes - Lecture 9: Asymptote

EXAMPLE 1 Use the guidelines to sketch the curve (A) The domain is {x1 x. 1-0) = {x | x-±1} = (-0, (B) The x- and y-intercepts are both 0 (C) Since r-x) =代x), the function is l-Select-- . The curve is symmetric about the y-axis o0) 4.x2 (D) lim 11m = 111m is a horizontal asymptote. Since the denominator is 0 when x = ±1, we Therefore the line y compute the following limits: 4.x2 4.22 1 4.r2 1 4.22 lin | Select--$ | lim--=1..-Select--$ Therefore the lines x =-1 and are vertical asymptotes. This information about limits and asymptotes enables us to draw the asymptotes in the top figure Video Example) Tutorial Online Textbook (E) f, (r) = 82(r2-1)-4r2 (2r) -82 Since f (x) >0 when x 0 (x1), fis increasing on (0, and ( ,) and decreasing on , and(

We will find the horizontal and vertical asymptotes of f(x) = At what x-value is f (r) undefined? 6 What is the limit of f(x) as x approaches this value from the LEFT? innity What is the limit of r as x approaches this value from the RIGHT? f ity The vertical asymptote occurs at = 6 (enter "infinity" or -infinity for ±00; enter undefined" if the limit is undefined). (e ter inf nity or infinity for ±oci e ter defined if the 1- t is undefined). if there is no vertical asymptote, enter "none") im f(x)- (enter "infinity" or "-infinity" for ±00; enter "undefined" if the limit is undefined). (enter "infinity" or "-infinity" for The horizontal asymptote occurs at y =-1 if there is no horizontal asymptote, enter none") ote: You can earn partial credit on this problem Preview Answers Subnit answers You have attempted this problem 6 times Your overall recorded score is 71%. You have 4 attempts remaining Email instructor

Homework 45 ← → cl 슐 Secure l https://www.webassign.net/web/Student/Assignm 回Show My Work (optional ) 9. O 23 points SCalcCC4 4.5.003 Consider the given limits (a is a constant) lim / (z)=0 limp(r) Evaluate each limit below. If a limit is indeterminate, enter INDETERMINATE. (If you ling (z) = 0 lim h(x)-1 lim 9 (1)-00 limlf(z) -p(a) INFINITY lim pLr NFINITY Show My Work optionen⑦ 10. 1/1 points Previous Answers SCalcCo4 4 5.005 MI Evaluate the limit. (1f you need to use - on o, enter -INFINITY or INFINITY.)