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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→0+(cosh⁡(x)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
02468-8-6-4-2-1010-20002000
Plot the graph
Rapid solution [src] 
oo
∞\infty
Expand and simplify
One‐sided limits [src] 
     /cosh(x)\
 lim |-------|
x->0+\   x   /
lim⁡x→0+(cosh⁡(x)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→0−(cosh⁡(x)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→0−(cosh⁡(x)x)=∞\lim_{x \to 0^-}\left(\frac{\cosh{\left(x \right)}}{x}\right) = \infty
More at x→0 from the left
lim⁡x→0+(cosh⁡(x)x)=∞\lim_{x \to 0^+}\left(\frac{\cosh{\left(x \right)}}{x}\right) = \infty
lim⁡x→∞(cosh⁡(x)x)=∞\lim_{x \to \infty}\left(\frac{\cosh{\left(x \right)}}{x}\right) = \infty
More at x→oo
lim⁡x→1−(cosh⁡(x)x)=1+e22e\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→1+(cosh⁡(x)x)=1+e22e\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→−∞(cosh⁡(x)x)=−∞\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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