Calculus MTH 250 Lecture 5 Previous Lectures Summary

Previous Lecture’s Summary • Logarithmic functions. • Inverse trigonometric functions • Introduction to limits

Today’s Lecture • Some working rules • Limit at infinity • Horizontal asymptotes •

Horizontal asymptotes Consider: Ø If you examine the degree of the numerator and denominator,

Lecture Summary • Working rules for limits • Limit at infinity • Horizontal asymptotes

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Calculus (MTH 250) Lecture 5

Previous Lecture’s Summary • Logarithmic functions. • Inverse trigonometric functions • Introduction to limits • One sided limits • Limits that don’t exist • Vertical asymptotes • Laws of limit

Today’s Lecture • Some working rules • Limit at infinity • Horizontal asymptotes • Laws of Limit at infinity • Limits of log and exp functions • Formal definition of limit • Uniqueness of a Limit

Some working rules

Limit at infinity

Horizontal asymptotes

Horizontal asymptotes Consider: Ø If you examine the degree of the numerator and denominator, there’s one of three possibilities: 1. n > m: The degree of the numerator is bigger than the denominator (top heavy) a) L= There is no horizontal asymptote 2. n < m: The degree of the numerator is smaller than the denominator (bottom heavy) a) L=0 The horizontal asymptote is y = 0 3. n = m: The degree of the numerator is equal to the denominator a) L= The horizontal asymptote is y =

Laws of limits at infinity

Limits of Log and Exp functions

Formal definition of limit

Uniqueness of limit

Lecture Summary • Working rules for limits • Limit at infinity • Horizontal asymptotes • Laws of Limit at infinity • Limits of log and exp functions • Formal definition of limit • Uniqueness of a Limit