Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (-exp(-x)+exp(x))/(exp(x)+exp(-x))
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Limit of (3+3*x^3+5*x+5*x^2)/(-1+x^2)
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Limit of (3-x^2+5*x)/(4*x^7+81*x)
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Limit of -cos(1/x)+2*x*sin(1/x)
- Derivative of:
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log(cot(x))
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Identical expressions
- log(cot(x))
- logarithm of ( cotangent of (x))
- logcotx
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Similar expressions
- log(cot(x)^tan(x))
Limit of the function log(cot(x))
The solution
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lim log(cot(x)) x->0+
$$\lim_{x \to 0^+} \log{\left(\cot{\left(x \right)} \right)}$$
Limit(log(cot(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
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-} \log{\left(\cot{\left(x \right)} \right)} = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+} \log{\left(\cot{\left(x \right)} \right)} = \infty$$
$$\lim_{x \to \infty} \log{\left(\cot{\left(x \right)} \right)}$$
More at x→oo
$$\lim_{x \to 1^-} \log{\left(\cot{\left(x \right)} \right)} = - \log{\left(\tan{\left(1 \right)} \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \log{\left(\cot{\left(x \right)} \right)} = - \log{\left(\tan{\left(1 \right)} \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \log{\left(\cot{\left(x \right)} \right)}$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+} \log{\left(\cot{\left(x \right)} \right)} = \infty$$
$$\lim_{x \to \infty} \log{\left(\cot{\left(x \right)} \right)}$$
More at x→oo
$$\lim_{x \to 1^-} \log{\left(\cot{\left(x \right)} \right)} = - \log{\left(\tan{\left(1 \right)} \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \log{\left(\cot{\left(x \right)} \right)} = - \log{\left(\tan{\left(1 \right)} \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \log{\left(\cot{\left(x \right)} \right)}$$
More at x→-oo
One‐sided limits
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lim log(cot(x)) x->0+
$$\lim_{x \to 0^+} \log{\left(\cot{\left(x \right)} \right)}$$
oo
$$\infty$$
= 8.87290808919806
lim log(cot(x)) x->0-
$$\lim_{x \to 0^-} \log{\left(\cot{\left(x \right)} \right)}$$
oo
$$\infty$$
= (8.87290808919806 + 3.14159265358979j)
= (8.87290808919806 + 3.14159265358979j)
The graph