GATE CSE 2015 Set 1 | Question: 4

Question

$\displaystyle \lim_{x\rightarrow \infty } x^{ \tfrac{1}{x}}$ is

• A. $\infty $
• B. $0$
• C. $1$
• D. Not defined

Answer 1

 

We can clearly see that the graph of $y=x^{\frac{1}{x}}$ is a straight line parallel to x- axis giving a constant value of y =1 for all the values of x.

So when x$\rightarrow \infty$ then also we will get y=1.

$\therefore y= _{ x\rightarrow \infty }^{lim}x^{\frac{1}{x}} = 1$

Answer 2

This is standard limit formula so answer will be 1