Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (1+3*x)^(5/x)
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Limit of e^(1+3*x)*(-1+x)
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Limit of x*sin(2*x)/3
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Limit of ((3+n)/(5+n))^(4+n)
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Identical expressions
- x*sin(two *x)/ three
- x multiply by sinus of (2 multiply by x) divide by 3
- x multiply by sinus of (two multiply by x) divide by three
- xsin(2x)/3
- xsin2x/3
- x*sin(2*x) divide by 3
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Similar expressions
- x*(sin(2*x)/3+sin(4*x)/3)
- x*sin(2*x/3)
- (-3+x)*sin(2*x/3)
Limit of the function x*sin(2*x)/3
The solution
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[src]
/x*sin(2*x)\ lim |----------| x->0+\ 3 /
$$\lim_{x \to 0^+}\left(\frac{x \sin{\left(2 x \right)}}{3}\right)$$
Limit((x*sin(2*x))/3, x, 0)
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
$$\lim_{x \to 0^-}\left(\frac{x \sin{\left(2 x \right)}}{3}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{x \sin{\left(2 x \right)}}{3}\right) = 0$$
$$\lim_{x \to \infty}\left(\frac{x \sin{\left(2 x \right)}}{3}\right) = \left\langle -\infty, \infty\right\rangle$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{x \sin{\left(2 x \right)}}{3}\right) = \frac{\sin{\left(2 \right)}}{3}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{x \sin{\left(2 x \right)}}{3}\right) = \frac{\sin{\left(2 \right)}}{3}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{x \sin{\left(2 x \right)}}{3}\right) = \left\langle -\infty, \infty\right\rangle$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{x \sin{\left(2 x \right)}}{3}\right) = 0$$
$$\lim_{x \to \infty}\left(\frac{x \sin{\left(2 x \right)}}{3}\right) = \left\langle -\infty, \infty\right\rangle$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{x \sin{\left(2 x \right)}}{3}\right) = \frac{\sin{\left(2 \right)}}{3}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{x \sin{\left(2 x \right)}}{3}\right) = \frac{\sin{\left(2 \right)}}{3}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{x \sin{\left(2 x \right)}}{3}\right) = \left\langle -\infty, \infty\right\rangle$$
More at x→-oo
One‐sided limits
[src]
/x*sin(2*x)\ lim |----------| x->0+\ 3 /
$$\lim_{x \to 0^+}\left(\frac{x \sin{\left(2 x \right)}}{3}\right)$$
0
$$0$$
= 1.28273154496427e-31
/x*sin(2*x)\ lim |----------| x->0-\ 3 /
$$\lim_{x \to 0^-}\left(\frac{x \sin{\left(2 x \right)}}{3}\right)$$
0
$$0$$
= 1.28273154496427e-31
= 1.28273154496427e-31
The graph