Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (10+12*x)/x^3
- Limit of (1+2*x/3)^(3251035981008077*x/140737488355328)
- Limit of (10+x)^(1/x)
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Limit of x^(3/2)*(sqrt(7+x^3)-sqrt(-1+x^3))
- Derivative of:
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2*sin(x)+sin(2*x)
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Identical expressions
- two *sin(x)+sin(two *x)
- 2 multiply by sinus of (x) plus sinus of (2 multiply by x)
- two multiply by sinus of (x) plus sinus of (two multiply by x)
- 2sin(x)+sin(2x)
- 2sinx+sin2x
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Similar expressions
- 2*sin(x)-sin(2*x)
- 2*sinx+sin(2*x)
Limit of the function 2*sin(x)+sin(2*x)
The solution
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lim (2*sin(x) + sin(2*x)) x->oo
$$\lim_{x \to \infty}\left(2 \sin{\left(x \right)} + \sin{\left(2 x \right)}\right)$$
Limit(2*sin(x) + 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
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to \infty}\left(2 \sin{\left(x \right)} + \sin{\left(2 x \right)}\right) = \left\langle -3, 3\right\rangle$$
$$\lim_{x \to 0^-}\left(2 \sin{\left(x \right)} + \sin{\left(2 x \right)}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(2 \sin{\left(x \right)} + \sin{\left(2 x \right)}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(2 \sin{\left(x \right)} + \sin{\left(2 x \right)}\right) = \sin{\left(2 \right)} + 2 \sin{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(2 \sin{\left(x \right)} + \sin{\left(2 x \right)}\right) = \sin{\left(2 \right)} + 2 \sin{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(2 \sin{\left(x \right)} + \sin{\left(2 x \right)}\right) = \left\langle -3, 3\right\rangle$$
More at x→-oo
$$\lim_{x \to 0^-}\left(2 \sin{\left(x \right)} + \sin{\left(2 x \right)}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(2 \sin{\left(x \right)} + \sin{\left(2 x \right)}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(2 \sin{\left(x \right)} + \sin{\left(2 x \right)}\right) = \sin{\left(2 \right)} + 2 \sin{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(2 \sin{\left(x \right)} + \sin{\left(2 x \right)}\right) = \sin{\left(2 \right)} + 2 \sin{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(2 \sin{\left(x \right)} + \sin{\left(2 x \right)}\right) = \left\langle -3, 3\right\rangle$$
More at x→-oo
The graph