Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (1-4*x)^(1/x)
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Limit of (-16+x^2+6*x)/(-2-5*x+3*x^2)
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Limit of (1+x)^(2/3)-(-1+x)^(2/3)
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Limit of 1/3+x/3
- Derivative of:
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asin(1/x)
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Identical expressions
- asin(one /x)
- arc sinus of e of (1 divide by x)
- arc sinus of e of (one divide by x)
- asin1/x
- asin(1 divide by x)
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Similar expressions
- arcsin(1/x)
Limit of the function asin(1/x)
The solution
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/1\ lim asin|-| x->oo \x/
$$\lim_{x \to \infty} \operatorname{asin}{\left(\frac{1}{x} \right)}$$
Limit(asin(1/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
$$\lim_{x \to \infty} \operatorname{asin}{\left(\frac{1}{x} \right)} = 0$$
$$\lim_{x \to 0^-} \operatorname{asin}{\left(\frac{1}{x} \right)} = \infty i$$
More at x→0 from the left
$$\lim_{x \to 0^+} \operatorname{asin}{\left(\frac{1}{x} \right)} = - \infty i$$
More at x→0 from the right
$$\lim_{x \to 1^-} \operatorname{asin}{\left(\frac{1}{x} \right)} = \frac{\pi}{2}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \operatorname{asin}{\left(\frac{1}{x} \right)} = \frac{\pi}{2}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \operatorname{asin}{\left(\frac{1}{x} \right)} = 0$$
More at x→-oo
$$\lim_{x \to 0^-} \operatorname{asin}{\left(\frac{1}{x} \right)} = \infty i$$
More at x→0 from the left
$$\lim_{x \to 0^+} \operatorname{asin}{\left(\frac{1}{x} \right)} = - \infty i$$
More at x→0 from the right
$$\lim_{x \to 1^-} \operatorname{asin}{\left(\frac{1}{x} \right)} = \frac{\pi}{2}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \operatorname{asin}{\left(\frac{1}{x} \right)} = \frac{\pi}{2}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \operatorname{asin}{\left(\frac{1}{x} \right)} = 0$$
More at x→-oo
The graph