Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of 7^(1/(-3+x))
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Limit of (3-3*x^2+4*x^4+6*x^3)/(2*x^2+7*x^4)
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Limit of ((5+4*x)/(-1+5*x))^(1+3*x)
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Limit of (-6-x^2-3*x+4*x^3)/(3-x^2+2*x^3)
- Graphing y =:
- x*(pi/2-atan(1/x))
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Identical expressions
- x*(pi/ two -atan(one /x))
- x multiply by ( Pi divide by 2 minus arc tangent of gent of (1 divide by x))
- x multiply by ( Pi divide by two minus arc tangent of gent of (one divide by x))
- x(pi/2-atan(1/x))
- xpi/2-atan1/x
- x*(pi divide by 2-atan(1 divide by x))
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Similar expressions
- x*(pi/2+atan(1/x))
- x*(pi/2-arctan(1/x))
Limit of the function x*(pi/2-atan(1/x))
The solution
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[src]
/ /pi / 1\\\ lim |x*|-- - atan|1*-||| x->0+\ \2 \ x///
$$\lim_{x \to 0^+}\left(x \left(- \operatorname{atan}{\left(1 \cdot \frac{1}{x} \right)} + \frac{\pi}{2}\right)\right)$$
Limit(x*(pi/2 - atan(1/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
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-}\left(x \left(- \operatorname{atan}{\left(1 \cdot \frac{1}{x} \right)} + \frac{\pi}{2}\right)\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x \left(- \operatorname{atan}{\left(1 \cdot \frac{1}{x} \right)} + \frac{\pi}{2}\right)\right) = 0$$
$$\lim_{x \to \infty}\left(x \left(- \operatorname{atan}{\left(1 \cdot \frac{1}{x} \right)} + \frac{\pi}{2}\right)\right) = \infty$$
More at x→oo
$$\lim_{x \to 1^-}\left(x \left(- \operatorname{atan}{\left(1 \cdot \frac{1}{x} \right)} + \frac{\pi}{2}\right)\right) = \frac{\pi}{4}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x \left(- \operatorname{atan}{\left(1 \cdot \frac{1}{x} \right)} + \frac{\pi}{2}\right)\right) = \frac{\pi}{4}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x \left(- \operatorname{atan}{\left(1 \cdot \frac{1}{x} \right)} + \frac{\pi}{2}\right)\right) = -\infty$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x \left(- \operatorname{atan}{\left(1 \cdot \frac{1}{x} \right)} + \frac{\pi}{2}\right)\right) = 0$$
$$\lim_{x \to \infty}\left(x \left(- \operatorname{atan}{\left(1 \cdot \frac{1}{x} \right)} + \frac{\pi}{2}\right)\right) = \infty$$
More at x→oo
$$\lim_{x \to 1^-}\left(x \left(- \operatorname{atan}{\left(1 \cdot \frac{1}{x} \right)} + \frac{\pi}{2}\right)\right) = \frac{\pi}{4}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x \left(- \operatorname{atan}{\left(1 \cdot \frac{1}{x} \right)} + \frac{\pi}{2}\right)\right) = \frac{\pi}{4}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x \left(- \operatorname{atan}{\left(1 \cdot \frac{1}{x} \right)} + \frac{\pi}{2}\right)\right) = -\infty$$
More at x→-oo
One‐sided limits
[src]
/ /pi / 1\\\ lim |x*|-- - atan|1*-||| x->0+\ \2 \ x///
$$\lim_{x \to 0^+}\left(x \left(- \operatorname{atan}{\left(1 \cdot \frac{1}{x} \right)} + \frac{\pi}{2}\right)\right)$$
0
$$0$$
= -1.52331055417713e-32
/ /pi / 1\\\ lim |x*|-- - atan|1*-||| x->0-\ \2 \ x///
$$\lim_{x \to 0^-}\left(x \left(- \operatorname{atan}{\left(1 \cdot \frac{1}{x} \right)} + \frac{\pi}{2}\right)\right)$$
0
$$0$$
= -4.21138056040416e-32
= -4.21138056040416e-32
The graph