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1/(1-cos(x))
Limit of the function/ 1/(1-cos(x))

Limit of the function 1/(1-cos(x))

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The solution

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         1     
 lim ----------
x->0+1 - cos(x)
lim⁡x→0+11−cos⁡(x)\lim_{x \to 0^+} \frac{1}{1 - \cos{\left(x \right)}} 
Limit(1/(1 - cos(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
02468-8-6-4-2-1010050000
Plot the graph
Other limits x→0, -oo, +oo, 1
lim⁡x→0−11−cos⁡(x)=∞\lim_{x \to 0^-} \frac{1}{1 - \cos{\left(x \right)}} = \infty
More at x→0 from the left
lim⁡x→0+11−cos⁡(x)=∞\lim_{x \to 0^+} \frac{1}{1 - \cos{\left(x \right)}} = \infty
lim⁡x→∞11−cos⁡(x)=⟨12,∞⟩\lim_{x \to \infty} \frac{1}{1 - \cos{\left(x \right)}} = \left\langle \frac{1}{2}, \infty\right\rangle
More at x→oo
lim⁡x→1−11−cos⁡(x)=−1−1+cos⁡(1)\lim_{x \to 1^-} \frac{1}{1 - \cos{\left(x \right)}} = - \frac{1}{-1 + \cos{\left(1 \right)}}
More at x→1 from the left
lim⁡x→1+11−cos⁡(x)=−1−1+cos⁡(1)\lim_{x \to 1^+} \frac{1}{1 - \cos{\left(x \right)}} = - \frac{1}{-1 + \cos{\left(1 \right)}}
More at x→1 from the right
lim⁡x→−∞11−cos⁡(x)=⟨12,∞⟩\lim_{x \to -\infty} \frac{1}{1 - \cos{\left(x \right)}} = \left\langle \frac{1}{2}, \infty\right\rangle
More at x→-oo
Rapid solution [src] 
oo
∞\infty
Expand and simplify
One‐sided limits [src] 
         1     
 lim ----------
x->0+1 - cos(x)
lim⁡x→0+11−cos⁡(x)\lim_{x \to 0^+} \frac{1}{1 - \cos{\left(x \right)}} 
oo
∞\infty 
= 45602.1666670322
         1     
 lim ----------
x->0-1 - cos(x)
lim⁡x→0−11−cos⁡(x)\lim_{x \to 0^-} \frac{1}{1 - \cos{\left(x \right)}} 
oo
∞\infty 
= 45602.1666670322
= 45602.1666670322
Numerical answer [src] 
45602.1666670322
45602.1666670322
The graph
Limit of the function 1/(1-cos(x))
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