Mister Exam

# Limit of the function cosh(1/x)

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### The solution

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         /1\
lim cosh|-|
x->oo    \x/
$$\lim_{x \to \infty} \cosh{\left(\frac{1}{x} \right)}$$
Limit(cosh(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
Rapid solution [src]
1
$$1$$
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to \infty} \cosh{\left(\frac{1}{x} \right)} = 1$$
$$\lim_{x \to 0^-} \cosh{\left(\frac{1}{x} \right)} = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+} \cosh{\left(\frac{1}{x} \right)} = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-} \cosh{\left(\frac{1}{x} \right)} = \frac{1 + e^{2}}{2 e}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \cosh{\left(\frac{1}{x} \right)} = \frac{1 + e^{2}}{2 e}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \cosh{\left(\frac{1}{x} \right)} = 1$$
More at x→-oo
The graph
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