Calculus 1000A/B Lecture Notes - Lecture 15: Asymptote

• School: Western University
• Department: Calculus
• Course: Calculus 1000A/B
• Professor: Kiriushcheva

Document Summary

Calculus 1000a lecture 15 - section 2. 6- limits at infinity continued. Recall: lim (cid:4666)(cid:1876)(cid:4667)= the horizontal asymptote (ha) is defined by y= l. 7(cid:3119)+(cid:2870) (cid:2869) = lim (cid:2870) (cid:3121)+(cid:3118)(cid:3119) (cid:3119)+(cid:2871)(cid:3118)+(cid:2873)= lim +(cid:3118)(cid:3118) (cid:3117)(cid:3119: lim (cid:3120)+(cid:2870) (cid:2869) (cid:2869)+(cid:3119)+(cid:3121)(cid:3119, therefore, lim (cid:2869)= the limit will be (cid:3121)+(cid:2873)(cid:3118) (cid:2869)= lim (cid:2869) (cid:3118)(cid:3118)+(cid:3117)(cid:3119, lim (cid:3119) (cid:2870)+(cid:2869) (cid:3118)+(cid:3121) (cid:3117)(cid:3119, therefore, lim (cid:2869)(cid:3118)=0 the limit will be zero (0). In examples where the numerator has a higher degree than the denominator: rational functions with the denominator having a higher degree than the numerator. In this case, we again divide top and bottom by the highest common power: again, (cid:858)x(cid:859) is growing sufficiently large, so we know that each number divided by some power of x will be zero. In examples where the denominator has a higher degree than the numerator: rational functions with the numerator having a higher degree than the denominator.