Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (-6+x^2-x)/(6+x^2-5*x)
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Limit of log(1+x^2)/(-e^(-x)+cos(3*x))
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Limit of (-1+e^(2*x))/(3*x)
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Limit of -2+|-2+x|/x
- Derivative of:
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x^5*cos(x)
- Integral of d{x}:
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x^5*cos(x)
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Identical expressions
- x^ five *cos(x)
- x to the power of 5 multiply by co sinus of e of (x)
- x to the power of five multiply by co sinus of e of (x)
- x5*cos(x)
- x5*cosx
- x⁵*cos(x)
- x^5cos(x)
- x5cos(x)
- x5cosx
- x^5cosx
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Similar expressions
- x^5*cosx
Limit of the function x^5*cos(x)
The solution
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/ 5 \ lim \x *cos(x)/ x->2+
$$\lim_{x \to 2^+}\left(x^{5} \cos{\left(x \right)}\right)$$
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
One‐sided limits
[src]
/ 5 \ lim \x *cos(x)/ x->2+
$$\lim_{x \to 2^+}\left(x^{5} \cos{\left(x \right)}\right)$$
32*cos(2)
$$32 \cos{\left(2 \right)}$$
= -13.3166987695086
/ 5 \ lim \x *cos(x)/ x->2-
$$\lim_{x \to 2^-}\left(x^{5} \cos{\left(x \right)}\right)$$
32*cos(2)
$$32 \cos{\left(2 \right)}$$
= -13.3166987695086
= -13.3166987695086
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 2^-}\left(x^{5} \cos{\left(x \right)}\right) = 32 \cos{\left(2 \right)}$$
More at x→2 from the left
$$\lim_{x \to 2^+}\left(x^{5} \cos{\left(x \right)}\right) = 32 \cos{\left(2 \right)}$$
$$\lim_{x \to \infty}\left(x^{5} \cos{\left(x \right)}\right) = \infty \operatorname{sign}{\left(\left\langle -1, 1\right\rangle \right)}$$
More at x→oo
$$\lim_{x \to 0^-}\left(x^{5} \cos{\left(x \right)}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x^{5} \cos{\left(x \right)}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x^{5} \cos{\left(x \right)}\right) = \cos{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x^{5} \cos{\left(x \right)}\right) = \cos{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x^{5} \cos{\left(x \right)}\right) = - \infty \operatorname{sign}{\left(\left\langle -1, 1\right\rangle \right)}$$
More at x→-oo
More at x→2 from the left
$$\lim_{x \to 2^+}\left(x^{5} \cos{\left(x \right)}\right) = 32 \cos{\left(2 \right)}$$
$$\lim_{x \to \infty}\left(x^{5} \cos{\left(x \right)}\right) = \infty \operatorname{sign}{\left(\left\langle -1, 1\right\rangle \right)}$$
More at x→oo
$$\lim_{x \to 0^-}\left(x^{5} \cos{\left(x \right)}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x^{5} \cos{\left(x \right)}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x^{5} \cos{\left(x \right)}\right) = \cos{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x^{5} \cos{\left(x \right)}\right) = \cos{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x^{5} \cos{\left(x \right)}\right) = - \infty \operatorname{sign}{\left(\left\langle -1, 1\right\rangle \right)}$$
More at x→-oo
The graph