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

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

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      / sin(x)\
 lim  |-------|
   pi |   2   |
x->--+\cos (x)/
   2
lim⁡x→π2+(sin⁡(x)cos⁡2(x))\lim_{x \to \frac{\pi}{2}^+}\left(\frac{\sin{\left(x \right)}}{\cos^{2}{\left(x \right)}}\right) 
Limit(sin(x)/(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
-3.0-2.5-2.0-1.5-1.0-0.50.00.51.01.52.02.53.0-2500025000
Plot the graph
Rapid solution [src] 
oo
∞\infty
Expand and simplify
One‐sided limits [src] 
      / sin(x)\
 lim  |-------|
   pi |   2   |
x->--+\cos (x)/
   2
lim⁡x→π2+(sin⁡(x)cos⁡2(x))\lim_{x \to \frac{\pi}{2}^+}\left(\frac{\sin{\left(x \right)}}{\cos^{2}{\left(x \right)}}\right) 
oo
∞\infty 
= 22800.8333307754
      / sin(x)\
 lim  |-------|
   pi |   2   |
x->---\cos (x)/
   2
lim⁡x→π2−(sin⁡(x)cos⁡2(x))\lim_{x \to \frac{\pi}{2}^-}\left(\frac{\sin{\left(x \right)}}{\cos^{2}{\left(x \right)}}\right) 
oo
∞\infty 
= 22800.8333307745
= 22800.8333307745
Other limits x→0, -oo, +oo, 1
lim⁡x→π2−(sin⁡(x)cos⁡2(x))=∞\lim_{x \to \frac{\pi}{2}^-}\left(\frac{\sin{\left(x \right)}}{\cos^{2}{\left(x \right)}}\right) = \infty
More at x→pi/2 from the left
lim⁡x→π2+(sin⁡(x)cos⁡2(x))=∞\lim_{x \to \frac{\pi}{2}^+}\left(\frac{\sin{\left(x \right)}}{\cos^{2}{\left(x \right)}}\right) = \infty
lim⁡x→∞(sin⁡(x)cos⁡2(x))=⟨−∞,∞⟩\lim_{x \to \infty}\left(\frac{\sin{\left(x \right)}}{\cos^{2}{\left(x \right)}}\right) = \left\langle -\infty, \infty\right\rangle
More at x→oo
lim⁡x→0−(sin⁡(x)cos⁡2(x))=0\lim_{x \to 0^-}\left(\frac{\sin{\left(x \right)}}{\cos^{2}{\left(x \right)}}\right) = 0
More at x→0 from the left
lim⁡x→0+(sin⁡(x)cos⁡2(x))=0\lim_{x \to 0^+}\left(\frac{\sin{\left(x \right)}}{\cos^{2}{\left(x \right)}}\right) = 0
More at x→0 from the right
lim⁡x→1−(sin⁡(x)cos⁡2(x))=sin⁡(1)cos⁡2(1)\lim_{x \to 1^-}\left(\frac{\sin{\left(x \right)}}{\cos^{2}{\left(x \right)}}\right) = \frac{\sin{\left(1 \right)}}{\cos^{2}{\left(1 \right)}}
More at x→1 from the left
lim⁡x→1+(sin⁡(x)cos⁡2(x))=sin⁡(1)cos⁡2(1)\lim_{x \to 1^+}\left(\frac{\sin{\left(x \right)}}{\cos^{2}{\left(x \right)}}\right) = \frac{\sin{\left(1 \right)}}{\cos^{2}{\left(1 \right)}}
More at x→1 from the right
lim⁡x→−∞(sin⁡(x)cos⁡2(x))=⟨−∞,∞⟩\lim_{x \to -\infty}\left(\frac{\sin{\left(x \right)}}{\cos^{2}{\left(x \right)}}\right) = \left\langle -\infty, \infty\right\rangle
More at x→-oo
Numerical answer [src] 
22800.8333307754
22800.8333307754
The graph
Limit of the function sin(x)/cos(x)^2
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