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

Limit of the function x*cos(2*x)

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You have entered [src] 
 lim  (x*cos(2*x))
x->-oo
lim⁡x→−∞(xcos⁡(2x))\lim_{x \to -\infty}\left(x \cos{\left(2 x \right)}\right) 
Limit(x*cos(2*x), x, -oo)
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⁡(2x))=⟨−∞,∞⟩\lim_{x \to -\infty}\left(x \cos{\left(2 x \right)}\right) = \left\langle -\infty, \infty\right\rangle
lim⁡x→∞(xcos⁡(2x))=⟨−∞,∞⟩\lim_{x \to \infty}\left(x \cos{\left(2 x \right)}\right) = \left\langle -\infty, \infty\right\rangle
More at x→oo
lim⁡x→0−(xcos⁡(2x))=0\lim_{x \to 0^-}\left(x \cos{\left(2 x \right)}\right) = 0
More at x→0 from the left
lim⁡x→0+(xcos⁡(2x))=0\lim_{x \to 0^+}\left(x \cos{\left(2 x \right)}\right) = 0
More at x→0 from the right
lim⁡x→1−(xcos⁡(2x))=cos⁡(2)\lim_{x \to 1^-}\left(x \cos{\left(2 x \right)}\right) = \cos{\left(2 \right)}
More at x→1 from the left
lim⁡x→1+(xcos⁡(2x))=cos⁡(2)\lim_{x \to 1^+}\left(x \cos{\left(2 x \right)}\right) = \cos{\left(2 \right)}
More at x→1 from the right
The graph
Limit of the function x*cos(2*x)
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