Mister Exam

Lang:

Limit of the function e^(2x)cos(x)

You have entered [src]

     / 2*x       \
 lim \E   *cos(x)/
x->oo

\lim_{x \to \infty}\left(e^{2 x} \cos{\left(x \right)}\right)

Limit(E^(2*x)*cos(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]

<-oo, oo>

\left\langle -\infty, \infty\right\rangle

Expand and simplify

Other limits x→0, -oo, +oo, 1

\lim_{x \to \infty}\left(e^{2 x} \cos{\left(x \right)}\right) = \left\langle -\infty, \infty\right\rangle

\lim_{x \to 0^-}\left(e^{2 x} \cos{\left(x \right)}\right) = 1

\lim_{x \to 0^+}\left(e^{2 x} \cos{\left(x \right)}\right) = 1

\lim_{x \to 1^-}\left(e^{2 x} \cos{\left(x \right)}\right) = e^{2} \cos{\left(1 \right)}

\lim_{x \to 1^+}\left(e^{2 x} \cos{\left(x \right)}\right) = e^{2} \cos{\left(1 \right)}

\lim_{x \to -\infty}\left(e^{2 x} \cos{\left(x \right)}\right) = 0

The graph

Limit of the function e^(2*x)*cos(x)