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

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

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The solution

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     / 5       \
 lim \x *cos(x)/
x->2+
lim⁡x→2+(x5cos⁡(x))\lim_{x \to 2^+}\left(x^{5} \cos{\left(x \right)}\right) 
Limit(x^5*cos(x), x, 2)
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
-4.0-3.0-2.0-1.04.00.01.02.03.0-10001000
Plot the graph
One‐sided limits [src] 
     / 5       \
 lim \x *cos(x)/
x->2+
lim⁡x→2+(x5cos⁡(x))\lim_{x \to 2^+}\left(x^{5} \cos{\left(x \right)}\right) 
32*cos(2)
32cos⁡(2)32 \cos{\left(2 \right)} 
= -13.3166987695086
     / 5       \
 lim \x *cos(x)/
x->2-
lim⁡x→2−(x5cos⁡(x))\lim_{x \to 2^-}\left(x^{5} \cos{\left(x \right)}\right) 
32*cos(2)
32cos⁡(2)32 \cos{\left(2 \right)} 
= -13.3166987695086
= -13.3166987695086
Rapid solution [src] 
32*cos(2)
32cos⁡(2)32 \cos{\left(2 \right)}
Expand and simplify
Other limits x→0, -oo, +oo, 1
lim⁡x→2−(x5cos⁡(x))=32cos⁡(2)\lim_{x \to 2^-}\left(x^{5} \cos{\left(x \right)}\right) = 32 \cos{\left(2 \right)}
More at x→2 from the left
lim⁡x→2+(x5cos⁡(x))=32cos⁡(2)\lim_{x \to 2^+}\left(x^{5} \cos{\left(x \right)}\right) = 32 \cos{\left(2 \right)}
lim⁡x→∞(x5cos⁡(x))=∞sign⁡(⟨−1,1⟩)\lim_{x \to \infty}\left(x^{5} \cos{\left(x \right)}\right) = \infty \operatorname{sign}{\left(\left\langle -1, 1\right\rangle \right)}
More at x→oo
lim⁡x→0−(x5cos⁡(x))=0\lim_{x \to 0^-}\left(x^{5} \cos{\left(x \right)}\right) = 0
More at x→0 from the left
lim⁡x→0+(x5cos⁡(x))=0\lim_{x \to 0^+}\left(x^{5} \cos{\left(x \right)}\right) = 0
More at x→0 from the right
lim⁡x→1−(x5cos⁡(x))=cos⁡(1)\lim_{x \to 1^-}\left(x^{5} \cos{\left(x \right)}\right) = \cos{\left(1 \right)}
More at x→1 from the left
lim⁡x→1+(x5cos⁡(x))=cos⁡(1)\lim_{x \to 1^+}\left(x^{5} \cos{\left(x \right)}\right) = \cos{\left(1 \right)}
More at x→1 from the right
lim⁡x→−∞(x5cos⁡(x))=−∞sign⁡(⟨−1,1⟩)\lim_{x \to -\infty}\left(x^{5} \cos{\left(x \right)}\right) = - \infty \operatorname{sign}{\left(\left\langle -1, 1\right\rangle \right)}
More at x→-oo
Numerical answer [src] 
-13.3166987695086
-13.3166987695086
The graph
Limit of the function x^5*cos(x)
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