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x^3*cos(x)
Limit of the function/ x^3*cos(x)

Limit of the function x^3*cos(x)

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     / 3       \
 lim \x *cos(x)/
x->oo
lim⁡x→∞(x3cos⁡(x))\lim_{x \to \infty}\left(x^{3} \cos{\left(x \right)}\right) 
Limit(x^3*cos(x), x, oo, dir='-')
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
02468-8-6-4-2-1010-20002000
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→∞(x3cos⁡(x))=∞sign⁡(⟨−1,1⟩)\lim_{x \to \infty}\left(x^{3} \cos{\left(x \right)}\right) = \infty \operatorname{sign}{\left(\left\langle -1, 1\right\rangle \right)}
lim⁡x→0−(x3cos⁡(x))=0\lim_{x \to 0^-}\left(x^{3} \cos{\left(x \right)}\right) = 0
More at x→0 from the left
lim⁡x→0+(x3cos⁡(x))=0\lim_{x \to 0^+}\left(x^{3} \cos{\left(x \right)}\right) = 0
More at x→0 from the right
lim⁡x→1−(x3cos⁡(x))=cos⁡(1)\lim_{x \to 1^-}\left(x^{3} \cos{\left(x \right)}\right) = \cos{\left(1 \right)}
More at x→1 from the left
lim⁡x→1+(x3cos⁡(x))=cos⁡(1)\lim_{x \to 1^+}\left(x^{3} \cos{\left(x \right)}\right) = \cos{\left(1 \right)}
More at x→1 from the right
lim⁡x→−∞(x3cos⁡(x))=−∞sign⁡(⟨−1,1⟩)\lim_{x \to -\infty}\left(x^{3} \cos{\left(x \right)}\right) = - \infty \operatorname{sign}{\left(\left\langle -1, 1\right\rangle \right)}
More at x→-oo
The graph
Limit of the function x^3*cos(x)
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