Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of 2^(-n)*2^(1+n)
- Limit of tan(k*x)/x
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Limit of (-x+tan(x))/(x+2*sin(x))
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Limit of asin(5*x)/tan(3*x)
- Graphing y =:
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x^2*sin(2*x)
- Integral of d{x}:
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x^2*sin(2*x)
- Derivative of:
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x^2*sin(2*x)
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Identical expressions
- x^ two *sin(two *x)
- x squared multiply by sinus of (2 multiply by x)
- x to the power of two multiply by sinus of (two multiply by x)
- x2*sin(2*x)
- x2*sin2*x
- x²*sin(2*x)
- x to the power of 2*sin(2*x)
- x^2sin(2x)
- x2sin(2x)
- x2sin2x
- x^2sin2x
Limit of the function x^2*sin(2*x)
The solution
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/ 2 \ lim \x *sin(2*x)/ x->oo
$$\lim_{x \to \infty}\left(x^{2} \sin{\left(2 x \right)}\right)$$
Limit(x^2*sin(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
Rapid solution
[src]
oo*sign(<-1, 1>)
$$\infty \operatorname{sign}{\left(\left\langle -1, 1\right\rangle \right)}$$
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to \infty}\left(x^{2} \sin{\left(2 x \right)}\right) = \infty \operatorname{sign}{\left(\left\langle -1, 1\right\rangle \right)}$$
$$\lim_{x \to 0^-}\left(x^{2} \sin{\left(2 x \right)}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x^{2} \sin{\left(2 x \right)}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x^{2} \sin{\left(2 x \right)}\right) = \sin{\left(2 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x^{2} \sin{\left(2 x \right)}\right) = \sin{\left(2 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x^{2} \sin{\left(2 x \right)}\right) = \infty \operatorname{sign}{\left(\left\langle -1, 1\right\rangle \right)}$$
More at x→-oo
$$\lim_{x \to 0^-}\left(x^{2} \sin{\left(2 x \right)}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x^{2} \sin{\left(2 x \right)}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x^{2} \sin{\left(2 x \right)}\right) = \sin{\left(2 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x^{2} \sin{\left(2 x \right)}\right) = \sin{\left(2 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x^{2} \sin{\left(2 x \right)}\right) = \infty \operatorname{sign}{\left(\left\langle -1, 1\right\rangle \right)}$$
More at x→-oo
The graph