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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
$$\lim_{x \to -\infty}\left(x \sin{\left(2 x \right)}\right)$$ 
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
Plot the graph
Rapid solution [src] 
-oo*sign(<-1, 1>)
$$- \infty \operatorname{sign}{\left(\left\langle -1, 1\right\rangle \right)}$$
Expand and simplify
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to -\infty}\left(x \sin{\left(2 x \right)}\right) = - \infty \operatorname{sign}{\left(\left\langle -1, 1\right\rangle \right)}$$
$$\lim_{x \to \infty}\left(x \sin{\left(2 x \right)}\right) = \infty \operatorname{sign}{\left(\left\langle -1, 1\right\rangle \right)}$$
More at x→oo
$$\lim_{x \to 0^-}\left(x \sin{\left(2 x \right)}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x \sin{\left(2 x \right)}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x \sin{\left(2 x \right)}\right) = \sin{\left(2 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x \sin{\left(2 x \right)}\right) = \sin{\left(2 \right)}$$
More at x→1 from the right
The graph
Limit of the function x*sin(2*x)
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