Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of ((-2+x)/(1+x))^(-3+2*x)
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Limit of (-2*asin(x)+asin(2*x))/x^3
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Limit of (1/x)^(1/x)
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Limit of (-2-3*x+2*x^2)/(2+x^2-3*x)
- Graphing y =:
- acos(2*x)
- Derivative of:
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acos(2*x)
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Identical expressions
- acos(two *x)
- arc co sinus of e of ine of (2 multiply by x)
- arc co sinus of e of ine of (two multiply by x)
- acos(2x)
- acos2x
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Similar expressions
- arccos(2*x)
Limit of the function acos(2*x)
The solution
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lim acos(2*x) x->0+
$$\lim_{x \to 0^+} \operatorname{acos}{\left(2 x \right)}$$
Limit(acos(2*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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lim acos(2*x) x->0+
$$\lim_{x \to 0^+} \operatorname{acos}{\left(2 x \right)}$$
pi -- 2
$$\frac{\pi}{2}$$
= 1.5707963267949
lim acos(2*x) x->0-
$$\lim_{x \to 0^-} \operatorname{acos}{\left(2 x \right)}$$
pi -- 2
$$\frac{\pi}{2}$$
= 1.5707963267949
= 1.5707963267949
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-} \operatorname{acos}{\left(2 x \right)} = \frac{\pi}{2}$$
More at x→0 from the left
$$\lim_{x \to 0^+} \operatorname{acos}{\left(2 x \right)} = \frac{\pi}{2}$$
$$\lim_{x \to \infty} \operatorname{acos}{\left(2 x \right)} = \infty i$$
More at x→oo
$$\lim_{x \to 1^-} \operatorname{acos}{\left(2 x \right)} = i \log{\left(\sqrt{3} + 2 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \operatorname{acos}{\left(2 x \right)} = i \log{\left(\sqrt{3} + 2 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \operatorname{acos}{\left(2 x \right)} = - \infty i$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+} \operatorname{acos}{\left(2 x \right)} = \frac{\pi}{2}$$
$$\lim_{x \to \infty} \operatorname{acos}{\left(2 x \right)} = \infty i$$
More at x→oo
$$\lim_{x \to 1^-} \operatorname{acos}{\left(2 x \right)} = i \log{\left(\sqrt{3} + 2 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \operatorname{acos}{\left(2 x \right)} = i \log{\left(\sqrt{3} + 2 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \operatorname{acos}{\left(2 x \right)} = - \infty i$$
More at x→-oo
The graph