Answer
$$\infty $$
Work Step by Step
$$\eqalign{
& \mathop {\lim }\limits_{x \to \infty } 3{x^{11}} \cr
& = 3\mathop {\lim }\limits_{x \to \infty } {x^{11}} \cr
& {\text{Evaluate the limit, use the property of Theorem 2}}{\text{.6}} \cr
& \mathop {\lim }\limits_{x \to \infty } {x^n} = \infty ,{\text{ when }}n{\text{ is odd}}{\text{. Then,}} \cr
& 3\mathop {\lim }\limits_{x \to \infty } {x^{11}} = 3\left( \infty \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \infty \cr
& \cr
& \mathop {\lim }\limits_{x \to \infty } 3{x^{11}} = \infty \cr} $$
