Describe the end behavior of the function.
-$$f ( x ) = 2 x ^ { - 1 } \cos 2 x$$
A) $\lim _ { x \rightarrow \infty } f ( x ) = 2 ; \lim _ { x \rightarrow } f ( x ) = 2$
B) $\lim _ { x \rightarrow \infty } f ( x ) = 0 ; \lim _ { x \rightarrow \infty } f ( x ) = 0$
C) $\lim _ { x \rightarrow \infty } f ( x ) = - \infty ; \lim _ { x \rightarrow \infty } f ( x ) = \infty$
D) $\lim _ { x \rightarrow \infty } f ( x ) = 0 ; \lim _ { x \rightarrow \infty } f ( x ) = 2$

Question

Quizplus · Accepted Answer

The function $f(x) = 2x^{-1}\cos(2x)$ has a factor of $x^{-1}$, which approaches 0 as $x$ approaches infinity. The $\cos(2x)$ part oscillates between -1 and 1, so its product with $2x^{-1}$ also approaches 0 as $x$ approaches infinity or negative infinity.

Describe the End Behavior of the Function f(x)=2x−1cos⁡2xf ( x ) = 2 x ^ { - 1 } \cos 2 xf(x)=2x−1cos2x

Describe the End Behavior of the Function $f ( x ) = 2 x ^ { - 1 } \cos 2 x$