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x*cos(5*x)
Limit of the function/ x*cos(5*x)

Limit of the function x*cos(5*x)

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The solution

You have entered [src] 
 lim (x*cos(5*x))
x->0+
$$\lim_{x \to 0^+}\left(x \cos{\left(5 x \right)}\right)$$ 
Limit(x*cos(5*x), x, 0)
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] 
0
$$0$$
Expand and simplify
One‐sided limits [src] 
 lim (x*cos(5*x))
x->0+
$$\lim_{x \to 0^+}\left(x \cos{\left(5 x \right)}\right)$$ 
0
$$0$$ 
= -3.74473575226818e-29
 lim (x*cos(5*x))
x->0-
$$\lim_{x \to 0^-}\left(x \cos{\left(5 x \right)}\right)$$ 
0
$$0$$ 
= 3.74473575226818e-29
= 3.74473575226818e-29
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-}\left(x \cos{\left(5 x \right)}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x \cos{\left(5 x \right)}\right) = 0$$
$$\lim_{x \to \infty}\left(x \cos{\left(5 x \right)}\right) = \left\langle -\infty, \infty\right\rangle$$
More at x→oo
$$\lim_{x \to 1^-}\left(x \cos{\left(5 x \right)}\right) = \cos{\left(5 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x \cos{\left(5 x \right)}\right) = \cos{\left(5 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x \cos{\left(5 x \right)}\right) = \left\langle -\infty, \infty\right\rangle$$
More at x→-oo
Numerical answer [src] 
-3.74473575226818e-29
-3.74473575226818e-29
The graph
Limit of the function x*cos(5*x)
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