Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
-
Limit of 10+x^2+3*x^3+8*x
-
Limit of (-2+sqrt(x))/(-4+x^2)
-
Limit of x+2*x^3+5*x^4-x^2/3
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Limit of (-x^3+2*x+5*x^4)/(1+x^4-8*x^3)
- Graphing y =:
- 2*cos(x)*sin(x)
- Integral of d{x}:
- 2*cos(x)*sin(x)
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Identical expressions
- two *cos(x)*sin(x)
- 2 multiply by co sinus of e of (x) multiply by sinus of (x)
- two multiply by co sinus of e of (x) multiply by sinus of (x)
- 2cos(x)sin(x)
- 2cosxsinx
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Similar expressions
- (7+2*cos(x))*sin(x)
- 2*cosx*sinx
Limit of the function 2*cos(x)*sin(x)
The solution
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lim (2*cos(x)*sin(x)) x->oo
$$\lim_{x \to \infty}\left(\sin{\left(x \right)} 2 \cos{\left(x \right)}\right)$$
Limit((2*cos(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
$$\lim_{x \to \infty}\left(\sin{\left(x \right)} 2 \cos{\left(x \right)}\right) = \left\langle -2, 2\right\rangle$$
$$\lim_{x \to 0^-}\left(\sin{\left(x \right)} 2 \cos{\left(x \right)}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\sin{\left(x \right)} 2 \cos{\left(x \right)}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\sin{\left(x \right)} 2 \cos{\left(x \right)}\right) = 2 \sin{\left(1 \right)} \cos{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\sin{\left(x \right)} 2 \cos{\left(x \right)}\right) = 2 \sin{\left(1 \right)} \cos{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\sin{\left(x \right)} 2 \cos{\left(x \right)}\right) = \left\langle -2, 2\right\rangle$$
More at x→-oo
$$\lim_{x \to 0^-}\left(\sin{\left(x \right)} 2 \cos{\left(x \right)}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\sin{\left(x \right)} 2 \cos{\left(x \right)}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\sin{\left(x \right)} 2 \cos{\left(x \right)}\right) = 2 \sin{\left(1 \right)} \cos{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\sin{\left(x \right)} 2 \cos{\left(x \right)}\right) = 2 \sin{\left(1 \right)} \cos{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\sin{\left(x \right)} 2 \cos{\left(x \right)}\right) = \left\langle -2, 2\right\rangle$$
More at x→-oo
The graph