Limits at Infinity Horizontal Asymptotes Calculus 3.5

Limits at infinity “end behavior” on an infinite interval What does the graph do as x approaches infinity or negative infinity? 2Calculus 3.5

Examples Evaluate the following limits 3Calculus 3.5

Limits at Infinity See page 197 4Calculus 3.5

Horizontal Asymptotes Occur when the limit as x approaches infinity or negative infinity exists and is equal to L Limit doesn’t increase or decrease without bound 5Calculus 3.5

Theorem 3.10 If r is a positive rational number and c is any real number, then Furthermore, if x r is defined when x < 0, then 6Calculus 3.5

Examples Find the limits 7Calculus 3.5

Indeterminate form Not enough information to know the limit Must do more work before taking the limit 8Calculus 3.5

Examples Find each of the limits 9Calculus 3.5

Guidelines Page 200 If degree of numerator < degree of denominator, then L = 0 If degree of num = degree of denom, then L = ratio of leading coefficients If degree of num > degree of denom, then L does not exist 10Calculus 3.5

Examples Find each of the limits 11Calculus 3.5