Functions Question 50

Question: $ \underset{x\to 0+}{\mathop{\lim }},\frac{x{e^{1/x}}}{1+{e^{1/x}}}= $

Options:

A) 0

B) 1

C) $ \infty $

D) None of these

Show Answer

Answer:

Correct Answer: A

Solution:

$ \underset{x\to 0+}{\mathop{\lim }},\frac{x}{1+{e^{-1/x}}}=0 $ as $ {e^{-1/x}}\to 0 $ when $ x\to {0^{+}} $