Limits Continuity And Differentiability Question 19
Question: Consider the following: 1. $ \underset{x\to 0}{\mathop{\lim }}\frac{1}{x} $ exists. 2. $ \underset{x\to 0}{\mathop{\lim }}{e^{\frac{1}{x}}} $ does not exist. Which of the above is/are correct?
Options:
A) 1 only
B) 2 only
C) Both 1 and 2
D) Neither 1 nor 2
Show Answer
Answer:
Correct Answer: B
Solution:
$ \underset{x\to 0}{\mathop{\lim }}\frac{1}{x}=\frac{1}{0}=\infty $ which does not exist. Hence, statement-1 is incorrect. Now, $ \underset{x\to 0}{\mathop{\lim }}{e^{1/x}}={e^{\infty }} $ which also does not exist. Hence, statement-2 is correct.
BETA
