Example 15

Evaluate

Solution : L =

Example 16 Evaluate ( x⁵ - x³ - 7x )

Solution : Let L = ( x⁵ - x³ - 7x )

Limits at infinity describe the behavior of functions when its independent variable increases or decreases without bound. In either cases if L is the limit then    f (x) = L    or    f (x) = L. (L = real number)

Also, f(x) said to have horizontal asymptote at f(x) = L.

So, in Example 12, f(x) has a horizontal asymptote at y = 1/4.

      in Example 13, f(x) has a horizontal asymptote at y = 8.

      in Example 14, it is y = c/2, c is a real number.

      in Example 15, f(x) has no asymptote as x increases       without bound.

      in Example 16, f(x) has no asymptote as x decreases       without bound.

Index

Chapter 3