MAT 21A Lecture 5: Math 21a Lecture 5 Asymptotes of Limits to Infinity
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Summary for 9/28 lecture: limx 0 sin x x. L: if p > 0, then limx , if limx f(x) = l or limx f(x) = l, then y = l is a horizontal asymptote for. Case i: deg p(x) < deg q(x). By dividing the numerator and denominator by the highest power in q(x), we conclude that limx . Case ii: deg p(x) = deg q(x). Q(x) = l. so y = l is a the highest power in q(x), we conclude that limx horizontal asymptote. Case iii: deg p(x) > deg q(x). By performing the long division, we can write. Q(x), where t(x) is the quotient and r(x) is the remainder in the long division. If t(x) is a constant, then we have a horizontal asymptote. If t(x) is linear, then it is a called an oblique asymptote.
