MAT 21A Lecture Notes - Lecture 7: Square Root, Asymptote

• School: UC-Davis
• Department: Mathematics
• Course: MAT 21A
• Professor: R.Thomas

Document Summary

Mat21a - lecture 7 - 2. 6: limits involving infinity part 2. A(cid:373)e tri(cid:272)k (cid:449)orks for e(cid:454)po(cid:374)e(cid:374)ts (cid:449)hi(cid:272)h are(cid:374)"t positi(cid:448)e i(cid:374)tegers: To find (cid:1864)(cid:1865) (cid:4666) (cid:4667), divide everything by the highest power in the denominator. Example 1: (cid:1864)(cid:1865) (cid:1007): (cid:1864)(cid:1865) . Get rid of negative exponents: (cid:1864)(cid:1865) . Divide by x: (cid:1864)(cid:1865) (cid:4666) (cid:1006) (cid:1005)+ (cid:1005) (cid:4666) (cid:4667), (cid:271)ut (cid:454) goes to the left (cid:862)fore(cid:448)er(cid:863) instead of right. (cid:4666) (cid:4667): same idea as (cid:1864)(cid:1865) (cid:1864)(cid:1865) . (cid:4666) (cid:4667)= l : in terms of an unknown (cid:2013)> (cid:1004), find m so that < . Left inequality: this is always true, therefore we ignore it. In terms of (cid:2013)> (cid:1004), find m so that < |(cid:4666) (cid:1005)onl y because we are finding the limit as x - . If (cid:2013)> (cid:1005), our formula for m does not work. Same as , but be careful with | | (cid:1006)(cid:4667)= (cid:1864)(cid:1865) (cid:4666) (cid:1006) (cid:1005)+ (cid:1005) (cid:4666)| | (cid:1005)+ (cid:1005)