Provide an appropriate response.
-If $\lim _ { x \rightarrow \theta ^ { - } } f ( x ) = 1$ and $f ( x )$ is an odd function, which of the following statements are true?
I. $\lim _ { x \rightarrow - \theta } f ( x ) = 1$
II. $\lim _ { x - \theta ^ { + } } f ( x ) = - 1$
III. $\lim _ { x \rightarrow - \theta } f ( x )$ does not exist.
A) I and III only
B) I and II only
C) II and III only
D) I, II, and III

Question

Quizplus · Accepted Answer

Since $f(x)$ is an odd function, $f(-x) = -f(x)$. Given $\lim _ { x \rightarrow \theta ^ { - } } f ( x ) = 1$, it follows that $\lim _ { x \rightarrow - \theta ^ { + } } f ( x ) = -1$. Thus, $\lim _ { x \rightarrow - \theta } f ( x )$ does not exist because the left and right limits at $-\theta$ are not equal.

Provide an Appropriate Response lim⁡x→θ−f(x)=1\lim _ { x \rightarrow \theta ^ { - } } f ( x ) = 1limx→θ−​f(x)=1

Provide an Appropriate Response $\lim _ { x \rightarrow \theta ^ { - } } f ( x ) = 1$