Mister Exam

Other calculators:


cos(x)^2/x

You entered:

cos(x)^2/x

What you mean?

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

at
v

For end points:

The graph:

from to

Piecewise:

The solution

You have entered [src]
     /   2   \
     |cos (x)|
 lim |-------|
x->oo\   x   /
limx(cos2(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
Rapid solution [src]
0
00
Other limits x→0, -oo, +oo, 1
limx(cos2(x)x)=0\lim_{x \to \infty}\left(\frac{\cos^{2}{\left(x \right)}}{x}\right) = 0
limx0(cos2(x)x)=\lim_{x \to 0^-}\left(\frac{\cos^{2}{\left(x \right)}}{x}\right) = -\infty
More at x→0 from the left
limx0+(cos2(x)x)=\lim_{x \to 0^+}\left(\frac{\cos^{2}{\left(x \right)}}{x}\right) = \infty
More at x→0 from the right
limx1(cos2(x)x)=cos2(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
limx1+(cos2(x)x)=cos2(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
limx(cos2(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