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Limit of the function/ x*cos(x)

Limit of the function x*cos(x)

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The solution

You have entered [src] 
 lim (x*cos(x))
x->oo
lim⁡x→∞(xcos⁡(x))\lim_{x \to \infty}\left(x \cos{\left(x \right)}\right) 
Limit(x*cos(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] 
<-oo, oo>
⟨−∞,∞⟩\left\langle -\infty, \infty\right\rangle
Expand and simplify
Other limits x→0, -oo, +oo, 1
lim⁡x→∞(xcos⁡(x))=⟨−∞,∞⟩\lim_{x \to \infty}\left(x \cos{\left(x \right)}\right) = \left\langle -\infty, \infty\right\rangle
lim⁡x→0−(xcos⁡(x))=0\lim_{x \to 0^-}\left(x \cos{\left(x \right)}\right) = 0
More at x→0 from the left
lim⁡x→0+(xcos⁡(x))=0\lim_{x \to 0^+}\left(x \cos{\left(x \right)}\right) = 0
More at x→0 from the right
lim⁡x→1−(xcos⁡(x))=cos⁡(1)\lim_{x \to 1^-}\left(x \cos{\left(x \right)}\right) = \cos{\left(1 \right)}
More at x→1 from the left
lim⁡x→1+(xcos⁡(x))=cos⁡(1)\lim_{x \to 1^+}\left(x \cos{\left(x \right)}\right) = \cos{\left(1 \right)}
More at x→1 from the right
lim⁡x→−∞(xcos⁡(x))=⟨−∞,∞⟩\lim_{x \to -\infty}\left(x \cos{\left(x \right)}\right) = \left\langle -\infty, \infty\right\rangle
More at x→-oo
The graph
Limit of the function x*cos(x)
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