Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of cos(x)*log(x)
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Limit of sin(z)
- Limit of -8
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Limit of cos(pi/n)
- Derivative of:
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cos(x)*log(x)
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Identical expressions
- cos(x)*log(x)
- co sinus of e of (x) multiply by logarithm of (x)
- cos(x)log(x)
- cosxlogx
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Similar expressions
- acos(x)^log(x)
- cos(x)*log(x-a)/log(-exp(a)+exp(x))
- cos(x)*log(x-a)/log(e^x-e^a)
- cosx*log(x)
Limit of the function cos(x)*log(x)
The solution
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[src]
lim (cos(x)*log(x)) x->0+
$$\lim_{x \to 0^+}\left(\log{\left(x \right)} \cos{\left(x \right)}\right)$$
Limit(cos(x)*log(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
One‐sided limits
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lim (cos(x)*log(x)) x->0+
$$\lim_{x \to 0^+}\left(\log{\left(x \right)} \cos{\left(x \right)}\right)$$
-oo
$$-\infty$$
= -8.85888306270682
lim (cos(x)*log(x)) x->0-
$$\lim_{x \to 0^-}\left(\log{\left(x \right)} \cos{\left(x \right)}\right)$$
-oo
$$-\infty$$
= (-8.8553295008311 + 3.13695664871034j)
= (-8.8553295008311 + 3.13695664871034j)
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-}\left(\log{\left(x \right)} \cos{\left(x \right)}\right) = -\infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\log{\left(x \right)} \cos{\left(x \right)}\right) = -\infty$$
$$\lim_{x \to \infty}\left(\log{\left(x \right)} \cos{\left(x \right)}\right) = \left\langle -\infty, \infty\right\rangle$$
More at x→oo
$$\lim_{x \to 1^-}\left(\log{\left(x \right)} \cos{\left(x \right)}\right) = 0$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\log{\left(x \right)} \cos{\left(x \right)}\right) = 0$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\log{\left(x \right)} \cos{\left(x \right)}\right) = \left\langle -\infty, \infty\right\rangle$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\log{\left(x \right)} \cos{\left(x \right)}\right) = -\infty$$
$$\lim_{x \to \infty}\left(\log{\left(x \right)} \cos{\left(x \right)}\right) = \left\langle -\infty, \infty\right\rangle$$
More at x→oo
$$\lim_{x \to 1^-}\left(\log{\left(x \right)} \cos{\left(x \right)}\right) = 0$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\log{\left(x \right)} \cos{\left(x \right)}\right) = 0$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\log{\left(x \right)} \cos{\left(x \right)}\right) = \left\langle -\infty, \infty\right\rangle$$
More at x→-oo
The graph