Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (-3*e^(4*x)-2*e^(-x)+5*e^(2*x))/(-4*sqrt(1+5*x)+4*cos(3*x)+5*sin(2*x))
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Limit of (2+x^2+3*x)/(2+2*x^2+5*x)
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Limit of 1+(4/3)^n
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Limit of (1+n)^2/(2*n^2)
- Graphing y =:
- 1/(1+e^(-x))
- Derivative of:
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1/(1+e^(-x))
- Integral of d{x}:
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1/(1+e^(-x))
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Identical expressions
- one /(one +e^(-x))
- 1 divide by (1 plus e to the power of ( minus x))
- one divide by (one plus e to the power of ( minus x))
- 1/(1+e(-x))
- 1/1+e-x
- 1/1+e^-x
- 1 divide by (1+e^(-x))
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Similar expressions
- 1/(1-e^(-x))
- 1/(1+e^(x))
Limit of the function 1/(1+e^(-x))
The solution
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1
lim -------
x->-oo -x
1 + E
$$\lim_{x \to -\infty} \frac{1}{1 + e^{- x}}$$
Limit(1/(1 + E^(-x)), x, -oo)
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
$$\lim_{x \to -\infty} \frac{1}{1 + e^{- x}} = 0$$
$$\lim_{x \to \infty} \frac{1}{1 + e^{- x}} = 1$$
More at x→oo
$$\lim_{x \to 0^-} \frac{1}{1 + e^{- x}} = \frac{1}{2}$$
More at x→0 from the left
$$\lim_{x \to 0^+} \frac{1}{1 + e^{- x}} = \frac{1}{2}$$
More at x→0 from the right
$$\lim_{x \to 1^-} \frac{1}{1 + e^{- x}} = \frac{e}{1 + e}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \frac{1}{1 + e^{- x}} = \frac{e}{1 + e}$$
More at x→1 from the right
$$\lim_{x \to \infty} \frac{1}{1 + e^{- x}} = 1$$
More at x→oo
$$\lim_{x \to 0^-} \frac{1}{1 + e^{- x}} = \frac{1}{2}$$
More at x→0 from the left
$$\lim_{x \to 0^+} \frac{1}{1 + e^{- x}} = \frac{1}{2}$$
More at x→0 from the right
$$\lim_{x \to 1^-} \frac{1}{1 + e^{- x}} = \frac{e}{1 + e}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \frac{1}{1 + e^{- x}} = \frac{e}{1 + e}$$
More at x→1 from the right
The graph