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(1+cos(x))/x^2
Limit of the function/ (1+cos(x))/x^2

Limit of the function (1+cos(x))/x^2

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     /1 + cos(x)\
 lim |----------|
x->0+|     2    |
     \    x     /
lim⁡x→0+(cos⁡(x)+1x2)\lim_{x \to 0^+}\left(\frac{\cos{\left(x \right)} + 1}{x^{2}}\right) 
Limit((1 + cos(x))/x^2, 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
02468-8-6-4-2-1010050000
Plot the graph
Rapid solution [src] 
oo
∞\infty
Expand and simplify
One‐sided limits [src] 
     /1 + cos(x)\
 lim |----------|
x->0+|     2    |
     \    x     /
lim⁡x→0+(cos⁡(x)+1x2)\lim_{x \to 0^+}\left(\frac{\cos{\left(x \right)} + 1}{x^{2}}\right) 
oo
∞\infty 
= 45601.5000018274
     /1 + cos(x)\
 lim |----------|
x->0-|     2    |
     \    x     /
lim⁡x→0−(cos⁡(x)+1x2)\lim_{x \to 0^-}\left(\frac{\cos{\left(x \right)} + 1}{x^{2}}\right) 
oo
∞\infty 
= 45601.5000018274
= 45601.5000018274
Other limits x→0, -oo, +oo, 1
lim⁡x→0−(cos⁡(x)+1x2)=∞\lim_{x \to 0^-}\left(\frac{\cos{\left(x \right)} + 1}{x^{2}}\right) = \infty
More at x→0 from the left
lim⁡x→0+(cos⁡(x)+1x2)=∞\lim_{x \to 0^+}\left(\frac{\cos{\left(x \right)} + 1}{x^{2}}\right) = \infty
lim⁡x→∞(cos⁡(x)+1x2)=0\lim_{x \to \infty}\left(\frac{\cos{\left(x \right)} + 1}{x^{2}}\right) = 0
More at x→oo
lim⁡x→1−(cos⁡(x)+1x2)=cos⁡(1)+1\lim_{x \to 1^-}\left(\frac{\cos{\left(x \right)} + 1}{x^{2}}\right) = \cos{\left(1 \right)} + 1
More at x→1 from the left
lim⁡x→1+(cos⁡(x)+1x2)=cos⁡(1)+1\lim_{x \to 1^+}\left(\frac{\cos{\left(x \right)} + 1}{x^{2}}\right) = \cos{\left(1 \right)} + 1
More at x→1 from the right
lim⁡x→−∞(cos⁡(x)+1x2)=0\lim_{x \to -\infty}\left(\frac{\cos{\left(x \right)} + 1}{x^{2}}\right) = 0
More at x→-oo
Numerical answer [src] 
45601.5000018274
45601.5000018274
The graph
Limit of the function (1+cos(x))/x^2
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