GATE CH 2023 | Question: 11

Question

Which one of the following is the CORRECT value of $y,$ as defined by the expression given below? 

$$y=\lim _{x \rightarrow 0} \frac{2 x}{e^x-1}$$

• A. $1$
• B. $2$
• C. $0$
• D. $\infty$ 

Answer 1

First apply limit & check (0/0)

Then apply L’Hospital Rule differentiate numerator & denominator seperately

 function will be 2/$e^x$

apply given  limit on new above function = 2 (Ans. will be B)