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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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     /    cos(x)\
 lim |1 - ------|
x->0+|       2  |
     \      x   /
lim⁡x→0+(1−cos⁡(x)x2)\lim_{x \to 0^+}\left(1 - \frac{\cos{\left(x \right)}}{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
02468-8-6-4-2-1010-2500025000
Plot the graph
One‐sided limits [src] 
     /    cos(x)\
 lim |1 - ------|
x->0+|       2  |
     \      x   /
lim⁡x→0+(1−cos⁡(x)x2)\lim_{x \to 0^+}\left(1 - \frac{\cos{\left(x \right)}}{x^{2}}\right) 
-oo
−∞-\infty 
= -22799.5000018274
     /    cos(x)\
 lim |1 - ------|
x->0-|       2  |
     \      x   /
lim⁡x→0−(1−cos⁡(x)x2)\lim_{x \to 0^-}\left(1 - \frac{\cos{\left(x \right)}}{x^{2}}\right) 
-oo
−∞-\infty 
= -22799.5000018274
= -22799.5000018274
Other limits x→0, -oo, +oo, 1
lim⁡x→0−(1−cos⁡(x)x2)=−∞\lim_{x \to 0^-}\left(1 - \frac{\cos{\left(x \right)}}{x^{2}}\right) = -\infty
More at x→0 from the left
lim⁡x→0+(1−cos⁡(x)x2)=−∞\lim_{x \to 0^+}\left(1 - \frac{\cos{\left(x \right)}}{x^{2}}\right) = -\infty
lim⁡x→∞(1−cos⁡(x)x2)=1\lim_{x \to \infty}\left(1 - \frac{\cos{\left(x \right)}}{x^{2}}\right) = 1
More at x→oo
lim⁡x→1−(1−cos⁡(x)x2)=1−cos⁡(1)\lim_{x \to 1^-}\left(1 - \frac{\cos{\left(x \right)}}{x^{2}}\right) = 1 - \cos{\left(1 \right)}
More at x→1 from the left
lim⁡x→1+(1−cos⁡(x)x2)=1−cos⁡(1)\lim_{x \to 1^+}\left(1 - \frac{\cos{\left(x \right)}}{x^{2}}\right) = 1 - \cos{\left(1 \right)}
More at x→1 from the right
lim⁡x→−∞(1−cos⁡(x)x2)=1\lim_{x \to -\infty}\left(1 - \frac{\cos{\left(x \right)}}{x^{2}}\right) = 1
More at x→-oo
Rapid solution [src] 
-oo
−∞-\infty
Expand and simplify
Numerical answer [src] 
-22799.5000018274
-22799.5000018274
The graph
Limit of the function 1-cos(x)/x^2
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