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cosh(x)/x
Limit of the function/ cosh(x)/x

Limit of the function cosh(x)/x

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     /cosh(x)\
 lim |-------|
x->0+\   x   /
$$\lim_{x \to 0^+}\left(\frac{\cosh{\left(x \right)}}{x}\right)$$ 
Limit(cosh(x)/x, x, 0)
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
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Rapid solution [src] 
oo
$$\infty$$
Expand and simplify
One‐sided limits [src] 
     /cosh(x)\
 lim |-------|
x->0+\   x   /
$$\lim_{x \to 0^+}\left(\frac{\cosh{\left(x \right)}}{x}\right)$$ 
oo
$$\infty$$ 
= 151.00331127038
     /cosh(x)\
 lim |-------|
x->0-\   x   /
$$\lim_{x \to 0^-}\left(\frac{\cosh{\left(x \right)}}{x}\right)$$ 
-oo
$$-\infty$$ 
= -151.00331127038
= -151.00331127038
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-}\left(\frac{\cosh{\left(x \right)}}{x}\right) = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\cosh{\left(x \right)}}{x}\right) = \infty$$
$$\lim_{x \to \infty}\left(\frac{\cosh{\left(x \right)}}{x}\right) = \infty$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{\cosh{\left(x \right)}}{x}\right) = \frac{1 + e^{2}}{2 e}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\cosh{\left(x \right)}}{x}\right) = \frac{1 + e^{2}}{2 e}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\cosh{\left(x \right)}}{x}\right) = -\infty$$
More at x→-oo
Numerical answer [src] 
151.00331127038
151.00331127038
The graph
Limit of the function cosh(x)/x
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