Question

If $\lim_{x \rightarrow \infty}$, then

• A. $\left( \frac{x + 6}{x + 1} \right)^{x + 4}$ is continuous and differentiable for all x in its domain
• B. $\lim_{x \rightarrow 2^{+}}$is continuous for all x in its domain but not differentiable at $\frac{\sin(x–2)}{(x–2)^{2}}$.
• C. ${\lim_{n \rightarrow \infty}}^{\frac{1}{n^{3}}}$is neither continuous nor differentiable at $\lim_{x \rightarrow 0}$
• D. None of these

Answer 1

Answer: (B)

$\lim_{x \rightarrow 2^{+}}$is continuous for all x in its domain but not

differentiable at $\frac{\sin(x–2)}{(x–2)^{2}}$.

Answer 2

It is evident from the graph of $f ( x )$ = $| \log | x | \mid$ that $f ( x )$ is everywhere continuous but not differentiable at $x = \pm 1$