Mister Exam

Lang:

Limit of the function/ 2^(1/x)

Limit of the function 2^(1/x)

You have entered [src]

     x ___
 lim \/ 2 
x->oo

\lim_{x \to \infty} 2^{\frac{1}{x}}

Limit(2^(1/x), x, oo, dir='-')

Lopital's rule

There is no sense to apply Lopital's rule to this function since there is no indeterminateness of 0/0 or oo/oo type

The graph

Plot the graph

Other limits x→0, -oo, +oo, 1

\lim_{x \to \infty} 2^{\frac{1}{x}} = 1

\lim_{x \to 0^-} 2^{\frac{1}{x}} = 0

\lim_{x \to 0^+} 2^{\frac{1}{x}} = \infty

\lim_{x \to 1^-} 2^{\frac{1}{x}} = 2

\lim_{x \to 1^+} 2^{\frac{1}{x}} = 2

\lim_{x \to -\infty} 2^{\frac{1}{x}} = 1

Rapid solution [src]

1

Expand and simplify

The graph