Mister Exam

Lang:

Limit of the function (1+e^x)^(1/x)

You have entered [src]

        ________
     x /      x 
 lim \/  1 + E  
x->oo

\lim_{x \to \infty} \left(e^{x} + 1\right)^{\frac{1}{x}}

Limit((1 + E^x)^(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

Rapid solution [src]

e

Expand and simplify

Other limits x→0, -oo, +oo, 1

\lim_{x \to \infty} \left(e^{x} + 1\right)^{\frac{1}{x}} = e

\lim_{x \to 0^-} \left(e^{x} + 1\right)^{\frac{1}{x}} = 0

\lim_{x \to 0^+} \left(e^{x} + 1\right)^{\frac{1}{x}} = \infty

\lim_{x \to 1^-} \left(e^{x} + 1\right)^{\frac{1}{x}} = 1 + e

\lim_{x \to 1^+} \left(e^{x} + 1\right)^{\frac{1}{x}} = 1 + e

\lim_{x \to -\infty} \left(e^{x} + 1\right)^{\frac{1}{x}} = 1

The graph