Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of sin(2*x)/(5*x)
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Limit of ((3+2*x)/(7+5*x))^(1+x)
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Limit of ((-5+2*x)/(3+2*x))^(7*x)
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Limit of (-6+x+x^2)/(3+x)
- Sum of series:
- x^n/(1+x^n)
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Identical expressions
- x^n/(one +x^n)
- x to the power of n divide by (1 plus x to the power of n)
- x to the power of n divide by (one plus x to the power of n)
- xn/(1+xn)
- xn/1+xn
- x^n/1+x^n
- x^n divide by (1+x^n)
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Similar expressions
- x^n/(1-x^n)
Limit of the function x^n/(1+x^n)
The solution
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/ n \
| x |
lim |------|
n->oo| n|
\1 + x /
$$\lim_{n \to \infty}\left(\frac{x^{n}}{x^{n} + 1}\right)$$
Limit(x^n/(1 + x^n), n, oo, dir='-')
Other limits n→0, -oo, +oo, 1
$$\lim_{n \to \infty}\left(\frac{x^{n}}{x^{n} + 1}\right)$$
$$\lim_{n \to 0^-}\left(\frac{x^{n}}{x^{n} + 1}\right) = \frac{1}{2}$$
More at n→0 from the left
$$\lim_{n \to 0^+}\left(\frac{x^{n}}{x^{n} + 1}\right) = \frac{1}{2}$$
More at n→0 from the right
$$\lim_{n \to 1^-}\left(\frac{x^{n}}{x^{n} + 1}\right) = \frac{x}{x + 1}$$
More at n→1 from the left
$$\lim_{n \to 1^+}\left(\frac{x^{n}}{x^{n} + 1}\right) = \frac{x}{x + 1}$$
More at n→1 from the right
$$\lim_{n \to -\infty}\left(\frac{x^{n}}{x^{n} + 1}\right)$$
More at n→-oo
$$\lim_{n \to 0^-}\left(\frac{x^{n}}{x^{n} + 1}\right) = \frac{1}{2}$$
More at n→0 from the left
$$\lim_{n \to 0^+}\left(\frac{x^{n}}{x^{n} + 1}\right) = \frac{1}{2}$$
More at n→0 from the right
$$\lim_{n \to 1^-}\left(\frac{x^{n}}{x^{n} + 1}\right) = \frac{x}{x + 1}$$
More at n→1 from the left
$$\lim_{n \to 1^+}\left(\frac{x^{n}}{x^{n} + 1}\right) = \frac{x}{x + 1}$$
More at n→1 from the right
$$\lim_{n \to -\infty}\left(\frac{x^{n}}{x^{n} + 1}\right)$$
More at n→-oo