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

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

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You have entered [src] 
 lim  (x*sin(2*x))
x->-oo
lim⁡x→−∞(xsin⁡(2x))\lim_{x \to -\infty}\left(x \sin{\left(2 x \right)}\right) 
Limit(x*sin(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*sign(<-1, 1>)
−∞sign⁡(⟨−1,1⟩)- \infty \operatorname{sign}{\left(\left\langle -1, 1\right\rangle \right)}
Expand and simplify
Other limits x→0, -oo, +oo, 1
lim⁡x→−∞(xsin⁡(2x))=−∞sign⁡(⟨−1,1⟩)\lim_{x \to -\infty}\left(x \sin{\left(2 x \right)}\right) = - \infty \operatorname{sign}{\left(\left\langle -1, 1\right\rangle \right)}
lim⁡x→∞(xsin⁡(2x))=∞sign⁡(⟨−1,1⟩)\lim_{x \to \infty}\left(x \sin{\left(2 x \right)}\right) = \infty \operatorname{sign}{\left(\left\langle -1, 1\right\rangle \right)}
More at x→oo
lim⁡x→0−(xsin⁡(2x))=0\lim_{x \to 0^-}\left(x \sin{\left(2 x \right)}\right) = 0
More at x→0 from the left
lim⁡x→0+(xsin⁡(2x))=0\lim_{x \to 0^+}\left(x \sin{\left(2 x \right)}\right) = 0
More at x→0 from the right
lim⁡x→1−(xsin⁡(2x))=sin⁡(2)\lim_{x \to 1^-}\left(x \sin{\left(2 x \right)}\right) = \sin{\left(2 \right)}
More at x→1 from the left
lim⁡x→1+(xsin⁡(2x))=sin⁡(2)\lim_{x \to 1^+}\left(x \sin{\left(2 x \right)}\right) = \sin{\left(2 \right)}
More at x→1 from the right
The graph
Limit of the function x*sin(2*x)
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