Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of ((1+x)/(1+2*x))^x
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Limit of (n/(1+n))^(5+3*n)
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Limit of (9^x-8^x)/asin(3*x)
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Limit of (-4+2*x+8*x^2)/(6+4*x)
- Derivative of:
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asin(x/2)
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Identical expressions
- asin(x/ two)
- arc sinus of e of (x divide by 2)
- arc sinus of e of (x divide by two)
- asinx/2
- asin(x divide by 2)
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Similar expressions
- arcsin(x/2)
Limit of the function asin(x/2)
The solution
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[src]
/x\ lim asin|-| x->2+ \2/
$$\lim_{x \to 2^+} \operatorname{asin}{\left(\frac{x}{2} \right)}$$
Limit(asin(x/2), x, 2)
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
$$\lim_{x \to 2^-} \operatorname{asin}{\left(\frac{x}{2} \right)} = \frac{\pi}{2}$$
More at x→2 from the left
$$\lim_{x \to 2^+} \operatorname{asin}{\left(\frac{x}{2} \right)} = \frac{\pi}{2}$$
$$\lim_{x \to \infty} \operatorname{asin}{\left(\frac{x}{2} \right)} = - \infty i$$
More at x→oo
$$\lim_{x \to 0^-} \operatorname{asin}{\left(\frac{x}{2} \right)} = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+} \operatorname{asin}{\left(\frac{x}{2} \right)} = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-} \operatorname{asin}{\left(\frac{x}{2} \right)} = \frac{\pi}{6}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \operatorname{asin}{\left(\frac{x}{2} \right)} = \frac{\pi}{6}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \operatorname{asin}{\left(\frac{x}{2} \right)} = \infty i$$
More at x→-oo
More at x→2 from the left
$$\lim_{x \to 2^+} \operatorname{asin}{\left(\frac{x}{2} \right)} = \frac{\pi}{2}$$
$$\lim_{x \to \infty} \operatorname{asin}{\left(\frac{x}{2} \right)} = - \infty i$$
More at x→oo
$$\lim_{x \to 0^-} \operatorname{asin}{\left(\frac{x}{2} \right)} = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+} \operatorname{asin}{\left(\frac{x}{2} \right)} = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-} \operatorname{asin}{\left(\frac{x}{2} \right)} = \frac{\pi}{6}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \operatorname{asin}{\left(\frac{x}{2} \right)} = \frac{\pi}{6}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \operatorname{asin}{\left(\frac{x}{2} \right)} = \infty i$$
More at x→-oo
One‐sided limits
[src]
/x\ lim asin|-| x->2+ \2/
$$\lim_{x \to 2^+} \operatorname{asin}{\left(\frac{x}{2} \right)}$$
pi -- 2
$$\frac{\pi}{2}$$
= (1.5707963267949 - 0.0141259745533598j)
/x\ lim asin|-| x->2- \2/
$$\lim_{x \to 2^-} \operatorname{asin}{\left(\frac{x}{2} \right)}$$
pi -- 2
$$\frac{\pi}{2}$$
= 1.55672424115329
= 1.55672424115329
Numerical answer
[src]
(1.5707963267949 - 0.0141259745533598j)
(1.5707963267949 - 0.0141259745533598j)
The graph