Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (-3+x^2-2*x)/(-3+x)
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Limit of 5^x-cos(x)
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Limit of (x/2)^(1/(-2+x))
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Limit of (1-3/x)^x
- Graphing y =:
- x*sin(x)^2
- Integral of d{x}:
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x*sin(x)^2
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Identical expressions
- x*sin(x)^ two
- x multiply by sinus of (x) squared
- x multiply by sinus of (x) to the power of two
- x*sin(x)2
- x*sinx2
- x*sin(x)²
- x*sin(x) to the power of 2
- xsin(x)^2
- xsin(x)2
- xsinx2
- xsinx^2
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Similar expressions
- x*sin(x^2)/3
- x*sinx^2
Limit of the function x*sin(x)^2
The solution
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[src]
/ 2 \ lim \x*sin (x)/ x->oo
$$\lim_{x \to \infty}\left(x \sin^{2}{\left(x \right)}\right)$$
Limit(x*sin(x)^2, 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
$$\lim_{x \to \infty}\left(x \sin^{2}{\left(x \right)}\right) = \infty \operatorname{sign}{\left(\left\langle 0, 1\right\rangle \right)}$$
$$\lim_{x \to 0^-}\left(x \sin^{2}{\left(x \right)}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x \sin^{2}{\left(x \right)}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x \sin^{2}{\left(x \right)}\right) = \sin^{2}{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x \sin^{2}{\left(x \right)}\right) = \sin^{2}{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x \sin^{2}{\left(x \right)}\right) = - \infty \operatorname{sign}{\left(\left\langle 0, 1\right\rangle \right)}$$
More at x→-oo
$$\lim_{x \to 0^-}\left(x \sin^{2}{\left(x \right)}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x \sin^{2}{\left(x \right)}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x \sin^{2}{\left(x \right)}\right) = \sin^{2}{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x \sin^{2}{\left(x \right)}\right) = \sin^{2}{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x \sin^{2}{\left(x \right)}\right) = - \infty \operatorname{sign}{\left(\left\langle 0, 1\right\rangle \right)}$$
More at x→-oo
Rapid solution
[src]
oo*sign(<0, 1>)
$$\infty \operatorname{sign}{\left(\left\langle 0, 1\right\rangle \right)}$$
The graph