Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (-5+7*n)/(2+n)
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Limit of (-64+4^x)/(-3+x)
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Limit of (-7+3*x^2+5*x)/(1+x+3*x^2)
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Limit of (-2+2*x^3+7*x)/(-4-x+3*x^3)
- Graphing y =:
- factorial(x)/(1+2^x)
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Identical expressions
- factorial(x)/(one + two ^x)
- factorial(x) divide by (1 plus 2 to the power of x)
- factorial(x) divide by (one plus two to the power of x)
- factorial(x)/(1+2x)
- factorialx/1+2x
- factorialx/1+2^x
- factorial(x) divide by (1+2^x)
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Similar expressions
- factorial(x)/(1-2^x)
Limit of the function factorial(x)/(1+2^x)
The solution
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/ x! \
lim |------|
x->oo| x|
\1 + 2 /
$$\lim_{x \to \infty}\left(\frac{x!}{2^{x} + 1}\right)$$
Limit(factorial(x)/(1 + 2^x), x, oo, dir='-')
The graph
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to \infty}\left(\frac{x!}{2^{x} + 1}\right) = \infty$$
$$\lim_{x \to 0^-}\left(\frac{x!}{2^{x} + 1}\right) = \frac{1}{2}$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{x!}{2^{x} + 1}\right) = \frac{1}{2}$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{x!}{2^{x} + 1}\right) = \frac{1}{3}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{x!}{2^{x} + 1}\right) = \frac{1}{3}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{x!}{2^{x} + 1}\right) = \left(-\infty\right)!$$
More at x→-oo
$$\lim_{x \to 0^-}\left(\frac{x!}{2^{x} + 1}\right) = \frac{1}{2}$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{x!}{2^{x} + 1}\right) = \frac{1}{2}$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{x!}{2^{x} + 1}\right) = \frac{1}{3}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{x!}{2^{x} + 1}\right) = \frac{1}{3}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{x!}{2^{x} + 1}\right) = \left(-\infty\right)!$$
More at x→-oo
The graph