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+5*x)/(-2+4*x))^(1+3*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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Identical expressions
- asin((one / two)^x)
- arc sinus of e of ((1 divide by 2) to the power of x)
- arc sinus of e of ((one divide by two) to the power of x)
- asin((1/2)x)
- asin1/2x
- asin1/2^x
- asin((1 divide by 2)^x)
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Similar expressions
- arcsin((1/2)^x)
Limit of the function asin((1/2)^x)
The solution
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/ -x\ lim asin\2 / x->oo
$$\lim_{x \to \infty} \operatorname{asin}{\left(\left(\frac{1}{2}\right)^{x} \right)}$$
Limit(asin((1/2)^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
$$\lim_{x \to \infty} \operatorname{asin}{\left(\left(\frac{1}{2}\right)^{x} \right)} = 0$$
$$\lim_{x \to 0^-} \operatorname{asin}{\left(\left(\frac{1}{2}\right)^{x} \right)} = \frac{\pi}{2}$$
More at x→0 from the left
$$\lim_{x \to 0^+} \operatorname{asin}{\left(\left(\frac{1}{2}\right)^{x} \right)} = \frac{\pi}{2}$$
More at x→0 from the right
$$\lim_{x \to 1^-} \operatorname{asin}{\left(\left(\frac{1}{2}\right)^{x} \right)} = \frac{\pi}{6}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \operatorname{asin}{\left(\left(\frac{1}{2}\right)^{x} \right)} = \frac{\pi}{6}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \operatorname{asin}{\left(\left(\frac{1}{2}\right)^{x} \right)} = - \infty i$$
More at x→-oo
$$\lim_{x \to 0^-} \operatorname{asin}{\left(\left(\frac{1}{2}\right)^{x} \right)} = \frac{\pi}{2}$$
More at x→0 from the left
$$\lim_{x \to 0^+} \operatorname{asin}{\left(\left(\frac{1}{2}\right)^{x} \right)} = \frac{\pi}{2}$$
More at x→0 from the right
$$\lim_{x \to 1^-} \operatorname{asin}{\left(\left(\frac{1}{2}\right)^{x} \right)} = \frac{\pi}{6}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \operatorname{asin}{\left(\left(\frac{1}{2}\right)^{x} \right)} = \frac{\pi}{6}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \operatorname{asin}{\left(\left(\frac{1}{2}\right)^{x} \right)} = - \infty i$$
More at x→-oo
The graph