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cos(x)^(-2)
Limit of the function/ cos(x)^(-2)

Limit of the function cos(x)^(-2)

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         1   
 lim  -------
   pi    2   
x->--+cos (x)
   2
lim⁡x→π2+1cos⁡2(x)\lim_{x \to \frac{\pi}{2}^+} \frac{1}{\cos^{2}{\left(x \right)}} 
Limit(cos(x)^(-2), x, pi/2)
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
-3.0-2.5-2.0-1.5-1.0-0.50.00.51.01.52.02.53.0025000
Plot the graph
Rapid solution [src] 
oo
∞\infty
Expand and simplify
Other limits x→0, -oo, +oo, 1
lim⁡x→π2−1cos⁡2(x)=∞\lim_{x \to \frac{\pi}{2}^-} \frac{1}{\cos^{2}{\left(x \right)}} = \infty
More at x→pi/2 from the left
lim⁡x→π2+1cos⁡2(x)=∞\lim_{x \to \frac{\pi}{2}^+} \frac{1}{\cos^{2}{\left(x \right)}} = \infty
lim⁡x→∞1cos⁡2(x)=⟨0,∞⟩\lim_{x \to \infty} \frac{1}{\cos^{2}{\left(x \right)}} = \left\langle 0, \infty\right\rangle
More at x→oo
lim⁡x→0−1cos⁡2(x)=1\lim_{x \to 0^-} \frac{1}{\cos^{2}{\left(x \right)}} = 1
More at x→0 from the left
lim⁡x→0+1cos⁡2(x)=1\lim_{x \to 0^+} \frac{1}{\cos^{2}{\left(x \right)}} = 1
More at x→0 from the right
lim⁡x→1−1cos⁡2(x)=1cos⁡2(1)\lim_{x \to 1^-} \frac{1}{\cos^{2}{\left(x \right)}} = \frac{1}{\cos^{2}{\left(1 \right)}}
More at x→1 from the left
lim⁡x→1+1cos⁡2(x)=1cos⁡2(1)\lim_{x \to 1^+} \frac{1}{\cos^{2}{\left(x \right)}} = \frac{1}{\cos^{2}{\left(1 \right)}}
More at x→1 from the right
lim⁡x→−∞1cos⁡2(x)=⟨0,∞⟩\lim_{x \to -\infty} \frac{1}{\cos^{2}{\left(x \right)}} = \left\langle 0, \infty\right\rangle
More at x→-oo
One‐sided limits [src] 
         1   
 lim  -------
   pi    2   
x->--+cos (x)
   2
lim⁡x→π2+1cos⁡2(x)\lim_{x \to \frac{\pi}{2}^+} \frac{1}{\cos^{2}{\left(x \right)}} 
oo
∞\infty 
= 22801.3333362576
         1   
 lim  -------
   pi    2   
x->---cos (x)
   2
lim⁡x→π2−1cos⁡2(x)\lim_{x \to \frac{\pi}{2}^-} \frac{1}{\cos^{2}{\left(x \right)}} 
oo
∞\infty 
= 22801.3333362568
= 22801.3333362568
Numerical answer [src] 
22801.3333362576
22801.3333362576
The graph
Limit of the function cos(x)^(-2)
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