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x^5*cos(x)

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

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     / 5       \
 lim \x *cos(x)/
x->2+           
limx2+(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
One‐sided limits [src]
     / 5       \
 lim \x *cos(x)/
x->2+           
limx2+(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-           
limx2(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)}
Other limits x→0, -oo, +oo, 1
limx2(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
limx2+(x5cos(x))=32cos(2)\lim_{x \to 2^+}\left(x^{5} \cos{\left(x \right)}\right) = 32 \cos{\left(2 \right)}
limx(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
limx0(x5cos(x))=0\lim_{x \to 0^-}\left(x^{5} \cos{\left(x \right)}\right) = 0
More at x→0 from the left
limx0+(x5cos(x))=0\lim_{x \to 0^+}\left(x^{5} \cos{\left(x \right)}\right) = 0
More at x→0 from the right
limx1(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
limx1+(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
limx(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)