Question

Consider the following:
(1) $\underset{x\to 0}{lim}\frac{1}{x}$ exist.
(2) $\underset{x\to 0}{lim}{e}^{\frac{1}{x}}$ does not exist.
Which of the above is/are correct?

• A. (1) only
• B. (2) only
• C. Both (1) and (2)
• D. Neither (1) nor (2)

Answer 1

Answer: (B)

(2) only

$\underset{x\to 0^{+}}{lim}\frac{1}{x}=\frac{1}{0}=+\infty$

$\underset{x\to 0^{-}}{lim}\frac{1}{x}=\frac{1}{-0}=-\infty$

LHL$\ne$RHL

$\Rightarrow$Limit at $x=0$ does not exist.