Mister Exam
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How to use it?
- Limit of the function:
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Limit of (-1+e^(2*x))/(3*x)
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Limit of (-1+3*x)/(5+x^2+7*x)
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Limit of 1+13*x/5
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Limit of (7+x+x^2)/(-1+e^x)
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Identical expressions
- acot(x)^tan(x)
- arcco tangent of gent of (x) to the power of tangent of (x)
- acot(x)tan(x)
- acotxtanx
- acotx^tanx
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Similar expressions
- arccot(x)^tan(x)
- arccotx^tan(x)
Limit of the function acot(x)^tan(x)
The solution
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tan(x) lim acot (x) x->0+
$$\lim_{x \to 0^+} \operatorname{acot}^{\tan{\left(x \right)}}{\left(x \right)}$$
Limit(acot(x)^tan(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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tan(x) lim acot (x) x->0+
$$\lim_{x \to 0^+} \operatorname{acot}^{\tan{\left(x \right)}}{\left(x \right)}$$
1
$$1$$
= 1.0
tan(x) lim acot (x) x->0-
$$\lim_{x \to 0^-} \operatorname{acot}^{\tan{\left(x \right)}}{\left(x \right)}$$
1
$$1$$
= (1.0 + 7.25708536419871e-27j)
= (1.0 + 7.25708536419871e-27j)
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-} \operatorname{acot}^{\tan{\left(x \right)}}{\left(x \right)} = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+} \operatorname{acot}^{\tan{\left(x \right)}}{\left(x \right)} = 1$$
$$\lim_{x \to \infty} \operatorname{acot}^{\tan{\left(x \right)}}{\left(x \right)}$$
More at x→oo
$$\lim_{x \to 1^-} \operatorname{acot}^{\tan{\left(x \right)}}{\left(x \right)} = \frac{\pi^{\tan{\left(1 \right)}}}{2^{2 \tan{\left(1 \right)}}}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \operatorname{acot}^{\tan{\left(x \right)}}{\left(x \right)} = \frac{\pi^{\tan{\left(1 \right)}}}{2^{2 \tan{\left(1 \right)}}}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \operatorname{acot}^{\tan{\left(x \right)}}{\left(x \right)}$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+} \operatorname{acot}^{\tan{\left(x \right)}}{\left(x \right)} = 1$$
$$\lim_{x \to \infty} \operatorname{acot}^{\tan{\left(x \right)}}{\left(x \right)}$$
More at x→oo
$$\lim_{x \to 1^-} \operatorname{acot}^{\tan{\left(x \right)}}{\left(x \right)} = \frac{\pi^{\tan{\left(1 \right)}}}{2^{2 \tan{\left(1 \right)}}}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \operatorname{acot}^{\tan{\left(x \right)}}{\left(x \right)} = \frac{\pi^{\tan{\left(1 \right)}}}{2^{2 \tan{\left(1 \right)}}}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \operatorname{acot}^{\tan{\left(x \right)}}{\left(x \right)}$$
More at x→-oo
The graph