Mister Exam
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How to use it?
- Limit of the function:
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Limit of (x-sin(x))/(x-tan(x))
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Limit of tanh(n)^(1/n)
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Limit of csch(x)
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Limit of sqrt(2)/2
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Identical expressions
- csch(x)
- cschx
Limit of the function csch(x)
The solution
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lim csch(x) x->oo
$$\lim_{x \to \infty} \operatorname{csch}{\left(x \right)}$$
Limit(csch(x), x, oo, dir='-')
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
$$\lim_{x \to \infty} \operatorname{csch}{\left(x \right)} = 0$$
$$\lim_{x \to 0^-} \operatorname{csch}{\left(x \right)} = -\infty$$
More at x→0 from the left
$$\lim_{x \to 0^+} \operatorname{csch}{\left(x \right)} = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-} \operatorname{csch}{\left(x \right)} = \frac{1}{\sinh{\left(1 \right)}}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \operatorname{csch}{\left(x \right)} = \frac{1}{\sinh{\left(1 \right)}}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \operatorname{csch}{\left(x \right)} = 0$$
More at x→-oo
$$\lim_{x \to 0^-} \operatorname{csch}{\left(x \right)} = -\infty$$
More at x→0 from the left
$$\lim_{x \to 0^+} \operatorname{csch}{\left(x \right)} = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-} \operatorname{csch}{\left(x \right)} = \frac{1}{\sinh{\left(1 \right)}}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \operatorname{csch}{\left(x \right)} = \frac{1}{\sinh{\left(1 \right)}}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \operatorname{csch}{\left(x \right)} = 0$$
More at x→-oo
The graph