Question

If $\underset{x\to \infty }{lim}f\left(x\right)\ne \pm \infty$, then $\underset{x\to \infty }{lim}{f}^{\prime }\left(x\right)=$ ?

• A. \N
• B. 1
• C. indeterminate
• D. $\underset{x\to \infty }{lim}f\left(x\right)$

Answer 1

The correct option is A \N

$\underset{x\to \infty }{lim}f\left(x\right)=a$, where $a$ is a finite value.
It means function $f\left(x\right)$ converges to $a$, when $x\to \infty$.
$f^{\prime }\left(x\right)$ represents the slope at tangent at a point $x$

$\Rightarrow$ Here, the tangent at infinity is line
$y=a$, which parallel to x - axis.
Slope at is 0.

Hence, $\underset{x\to \infty }{lim}{f}^{\prime }\left(x\right)=0$.