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Limit of the function cos(5*x)

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 lim cos(5*x)
x->oo

\lim_{x \to \infty} \cos{\left(5 x \right)}

Limit(cos(5*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} \cos{\left(5 x \right)} = \left\langle -1, 1\right\rangle

\lim_{x \to 0^-} \cos{\left(5 x \right)} = 1

\lim_{x \to 0^+} \cos{\left(5 x \right)} = 1

\lim_{x \to 1^-} \cos{\left(5 x \right)} = \cos{\left(5 \right)}

\lim_{x \to 1^+} \cos{\left(5 x \right)} = \cos{\left(5 \right)}

\lim_{x \to -\infty} \cos{\left(5 x \right)} = \left\langle -1, 1\right\rangle

Rapid solution [src]

<-1, 1>

\left\langle -1, 1\right\rangle

Expand and simplify

The graph