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)))
- Sum of series:
- sin(n*x)/n^2
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Identical expressions
- sin(n*x)/n^ two
- sinus of (n multiply by x) divide by n squared
- sinus of (n multiply by x) divide by n to the power of two
- sin(n*x)/n2
- sinn*x/n2
- sin(n*x)/n²
- sin(n*x)/n to the power of 2
- sin(nx)/n^2
- sin(nx)/n2
- sinnx/n2
- sinnx/n^2
- sin(n*x) divide by n^2
Limit of the function sin(n*x)/n^2
The solution
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/sin(n*x)\
lim |--------|
n->oo| 2 |
\ n /
$$\lim_{n \to \infty}\left(\frac{\sin{\left(n x \right)}}{n^{2}}\right)$$
Limit(sin(n*x)/n^2, n, oo, dir='-')
Other limits n→0, -oo, +oo, 1
$$\lim_{n \to \infty}\left(\frac{\sin{\left(n x \right)}}{n^{2}}\right) = \tilde{\infty} x \cos{\left(\tilde{\infty} x \right)}$$
$$\lim_{n \to 0^-}\left(\frac{\sin{\left(n x \right)}}{n^{2}}\right) = - \infty \operatorname{sign}{\left(x \right)}$$
More at n→0 from the left
$$\lim_{n \to 0^+}\left(\frac{\sin{\left(n x \right)}}{n^{2}}\right) = \infty \operatorname{sign}{\left(x \right)}$$
More at n→0 from the right
$$\lim_{n \to 1^-}\left(\frac{\sin{\left(n x \right)}}{n^{2}}\right) = \sin{\left(x \right)}$$
More at n→1 from the left
$$\lim_{n \to 1^+}\left(\frac{\sin{\left(n x \right)}}{n^{2}}\right) = \sin{\left(x \right)}$$
More at n→1 from the right
$$\lim_{n \to -\infty}\left(\frac{\sin{\left(n x \right)}}{n^{2}}\right) = \tilde{\infty} x \cos{\left(\tilde{\infty} x \right)}$$
More at n→-oo
$$\lim_{n \to 0^-}\left(\frac{\sin{\left(n x \right)}}{n^{2}}\right) = - \infty \operatorname{sign}{\left(x \right)}$$
More at n→0 from the left
$$\lim_{n \to 0^+}\left(\frac{\sin{\left(n x \right)}}{n^{2}}\right) = \infty \operatorname{sign}{\left(x \right)}$$
More at n→0 from the right
$$\lim_{n \to 1^-}\left(\frac{\sin{\left(n x \right)}}{n^{2}}\right) = \sin{\left(x \right)}$$
More at n→1 from the left
$$\lim_{n \to 1^+}\left(\frac{\sin{\left(n x \right)}}{n^{2}}\right) = \sin{\left(x \right)}$$
More at n→1 from the right
$$\lim_{n \to -\infty}\left(\frac{\sin{\left(n x \right)}}{n^{2}}\right) = \tilde{\infty} x \cos{\left(\tilde{\infty} x \right)}$$
More at n→-oo