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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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           2   
  lim   cos (x)
   -pi         
x->----+       
    2
lim⁡x→(−1)π2+cos⁡2(x)\lim_{x \to \frac{\left(-1\right) \pi}{2}^+} \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
-3.0-2.5-2.0-1.5-1.0-0.50.00.51.01.52.02.53.002
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Rapid solution [src] 
0
00
Expand and simplify
One‐sided limits [src] 
           2   
  lim   cos (x)
   -pi         
x->----+       
    2
lim⁡x→(−1)π2+cos⁡2(x)\lim_{x \to \frac{\left(-1\right) \pi}{2}^+} \cos^{2}{\left(x \right)} 
0
00 
= 1.88597981818432e-31
           2   
  lim   cos (x)
   -pi         
x->-----       
    2
lim⁡x→(−1)π2−cos⁡2(x)\lim_{x \to \frac{\left(-1\right) \pi}{2}^-} \cos^{2}{\left(x \right)} 
0
00 
= 1.88597981818432e-31
= 1.88597981818432e-31
Other limits x→0, -oo, +oo, 1
lim⁡x→(−1)π2−cos⁡2(x)=0\lim_{x \to \frac{\left(-1\right) \pi}{2}^-} \cos^{2}{\left(x \right)} = 0
More at x→-pi/2 from the left
lim⁡x→(−1)π2+cos⁡2(x)=0\lim_{x \to \frac{\left(-1\right) \pi}{2}^+} \cos^{2}{\left(x \right)} = 0
lim⁡x→∞cos⁡2(x)=⟨0,1⟩\lim_{x \to \infty} \cos^{2}{\left(x \right)} = \left\langle 0, 1\right\rangle
More at x→oo
lim⁡x→0−cos⁡2(x)=1\lim_{x \to 0^-} \cos^{2}{\left(x \right)} = 1
More at x→0 from the left
lim⁡x→0+cos⁡2(x)=1\lim_{x \to 0^+} \cos^{2}{\left(x \right)} = 1
More at x→0 from the right
lim⁡x→1−cos⁡2(x)=cos⁡2(1)\lim_{x \to 1^-} \cos^{2}{\left(x \right)} = \cos^{2}{\left(1 \right)}
More at x→1 from the left
lim⁡x→1+cos⁡2(x)=cos⁡2(1)\lim_{x \to 1^+} \cos^{2}{\left(x \right)} = \cos^{2}{\left(1 \right)}
More at x→1 from the right
lim⁡x→−∞cos⁡2(x)=⟨0,1⟩\lim_{x \to -\infty} \cos^{2}{\left(x \right)} = \left\langle 0, 1\right\rangle
More at x→-oo
Numerical answer [src] 
1.88597981818432e-31
1.88597981818432e-31
The graph
Limit of the function cos(x)^2
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