Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of x^2*(1/3-cos(8*x)/3)
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Limit of (-2+x^2-x)/(-2+x+3*x^2)
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Limit of (-1+sin(x))/cos(x)
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Limit of (-2*sin(x)+sin(2*x))/(x*log(cos(5*x)))
- Integral of d{x}:
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cos(2*x)*sin(x)
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Identical expressions
- cos(two *x)*sin(x)
- co sinus of e of (2 multiply by x) multiply by sinus of (x)
- co sinus of e of (two multiply by x) multiply by sinus of (x)
- cos(2x)sin(x)
- cos2xsinx
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Similar expressions
- -(1-cos(2*x))*sin(x)/x+tan(x)
- cos(2*x)*sinx
Limit of the function cos(2*x)*sin(x)
The solution
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lim (cos(2*x)*sin(x)) x->oo
$$\lim_{x \to \infty}\left(\sin{\left(x \right)} \cos{\left(2 x \right)}\right)$$
Limit(cos(2*x)*sin(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
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to \infty}\left(\sin{\left(x \right)} \cos{\left(2 x \right)}\right) = \left\langle -1, 1\right\rangle$$
$$\lim_{x \to 0^-}\left(\sin{\left(x \right)} \cos{\left(2 x \right)}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\sin{\left(x \right)} \cos{\left(2 x \right)}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\sin{\left(x \right)} \cos{\left(2 x \right)}\right) = \sin{\left(1 \right)} \cos{\left(2 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\sin{\left(x \right)} \cos{\left(2 x \right)}\right) = \sin{\left(1 \right)} \cos{\left(2 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\sin{\left(x \right)} \cos{\left(2 x \right)}\right) = \left\langle -1, 1\right\rangle$$
More at x→-oo
$$\lim_{x \to 0^-}\left(\sin{\left(x \right)} \cos{\left(2 x \right)}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\sin{\left(x \right)} \cos{\left(2 x \right)}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\sin{\left(x \right)} \cos{\left(2 x \right)}\right) = \sin{\left(1 \right)} \cos{\left(2 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\sin{\left(x \right)} \cos{\left(2 x \right)}\right) = \sin{\left(1 \right)} \cos{\left(2 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\sin{\left(x \right)} \cos{\left(2 x \right)}\right) = \left\langle -1, 1\right\rangle$$
More at x→-oo
The graph