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x*sin(3*x)
Limit of the function/ x*sin(3*x)

Limit of the function x*sin(3*x)

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  lim  (x*sin(3*x))
x->nan+
$$\lim_{x \to \text{NaN}^+}\left(x \sin{\left(3 x \right)}\right)$$ 
Limit(x*sin(3*x), x, nan)
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
One‐sided limits [src] 
  lim  (x*sin(3*x))
x->nan+
$$\lim_{x \to \text{NaN}^+}\left(x \sin{\left(3 x \right)}\right)$$ 
  lim  (x*sin(3*x))
x->nan+
$$\lim_{x \to \text{NaN}^+}\left(x \sin{\left(3 x \right)}\right)$$ 
  lim  (x*sin(3*x))
x->nan-
$$\lim_{x \to \text{NaN}^-}\left(x \sin{\left(3 x \right)}\right)$$ 
  lim  (x*sin(3*x))
x->nan-
$$\lim_{x \to \text{NaN}^-}\left(x \sin{\left(3 x \right)}\right)$$ 
Limit(x*sin(3*x), x, nan, dir='-')
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to \text{NaN}^-}\left(x \sin{\left(3 x \right)}\right) = \lim_{x \to \text{NaN}^+}\left(x \sin{\left(3 x \right)}\right)$$
More at x→nan from the left
$$\lim_{x \to \text{NaN}^+}\left(x \sin{\left(3 x \right)}\right)$$
$$\lim_{x \to \infty}\left(x \sin{\left(3 x \right)}\right) = \left\langle -\infty, \infty\right\rangle$$
More at x→oo
$$\lim_{x \to 0^-}\left(x \sin{\left(3 x \right)}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x \sin{\left(3 x \right)}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x \sin{\left(3 x \right)}\right) = \sin{\left(3 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x \sin{\left(3 x \right)}\right) = \sin{\left(3 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x \sin{\left(3 x \right)}\right) = \left\langle -\infty, \infty\right\rangle$$
More at x→-oo
Rapid solution [src] 
  lim  (x*sin(3*x))
x->nan+
$$\lim_{x \to \text{NaN}^+}\left(x \sin{\left(3 x \right)}\right)$$
Expand and simplify
The graph
Limit of the function x*sin(3*x)
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