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

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cos(x)^2/x

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cos(x)^2/x
 
cos(x)^(2/x)
 
cos(x)^(2/x)

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

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You have entered [src] 
     /   2   \
     |cos (x)|
 lim |-------|
x->oo\   x   /
lim⁡x→∞(cos⁡2(x)x)\lim_{x \to \infty}\left(\frac{\cos^{2}{\left(x \right)}}{x}\right) 
Limit(cos(x)^2/x, x, oo, dir='-')
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
02468-8-6-4-2-1010-2020
Plot the graph
Rapid solution [src] 
0
00
Expand and simplify
Other limits x→0, -oo, +oo, 1
lim⁡x→∞(cos⁡2(x)x)=0\lim_{x \to \infty}\left(\frac{\cos^{2}{\left(x \right)}}{x}\right) = 0
lim⁡x→0−(cos⁡2(x)x)=−∞\lim_{x \to 0^-}\left(\frac{\cos^{2}{\left(x \right)}}{x}\right) = -\infty
More at x→0 from the left
lim⁡x→0+(cos⁡2(x)x)=∞\lim_{x \to 0^+}\left(\frac{\cos^{2}{\left(x \right)}}{x}\right) = \infty
More at x→0 from the right
lim⁡x→1−(cos⁡2(x)x)=cos⁡2(1)\lim_{x \to 1^-}\left(\frac{\cos^{2}{\left(x \right)}}{x}\right) = \cos^{2}{\left(1 \right)}
More at x→1 from the left
lim⁡x→1+(cos⁡2(x)x)=cos⁡2(1)\lim_{x \to 1^+}\left(\frac{\cos^{2}{\left(x \right)}}{x}\right) = \cos^{2}{\left(1 \right)}
More at x→1 from the right
lim⁡x→−∞(cos⁡2(x)x)=0\lim_{x \to -\infty}\left(\frac{\cos^{2}{\left(x \right)}}{x}\right) = 0
More at x→-oo
The graph
Limit of the function cos(x)^2/x
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