Mister Exam

Lang:

Limit of the function/ e^(x/3)

Limit of the function e^(x/3)

You have entered [src]

      x
      -
      3
 lim E 
x->oo

\lim_{x \to \infty} e^{\frac{x}{3}}

Limit(E^(x/3), 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]

oo

\infty

Expand and simplify

Other limits x→0, -oo, +oo, 1

\lim_{x \to \infty} e^{\frac{x}{3}} = \infty

\lim_{x \to 0^-} e^{\frac{x}{3}} = 1

\lim_{x \to 0^+} e^{\frac{x}{3}} = 1

\lim_{x \to 1^-} e^{\frac{x}{3}} = e^{\frac{1}{3}}

\lim_{x \to 1^+} e^{\frac{x}{3}} = e^{\frac{1}{3}}

\lim_{x \to -\infty} e^{\frac{x}{3}} = 0

The graph