Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of exp(2*x)
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Limit of 2*x^2
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Limit of e^(-x)/x
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Limit of x^3-2*x^2
- Integral of d{x}:
- e^(-x)/x
- Derivative of:
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e^(-x)/x
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Identical expressions
- e^(-x)/x
- e to the power of ( minus x) divide by x
- e(-x)/x
- e-x/x
- e^-x/x
- e^(-x) divide by x
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Similar expressions
- e^(x)/x
Limit of the function e^(-x)/x
The solution
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[src]
/ -x\
|E |
lim |---|
x->oo\ x /
$$\lim_{x \to \infty}\left(\frac{e^{- x}}{x}\right)$$
Limit(E^(-x)/x, x, oo, dir='-')
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
$$\lim_{x \to \infty}\left(\frac{e^{- x}}{x}\right) = 0$$
$$\lim_{x \to 0^-}\left(\frac{e^{- x}}{x}\right) = -\infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{e^{- x}}{x}\right) = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{e^{- x}}{x}\right) = e^{-1}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{e^{- x}}{x}\right) = e^{-1}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{e^{- x}}{x}\right) = -\infty$$
More at x→-oo
$$\lim_{x \to 0^-}\left(\frac{e^{- x}}{x}\right) = -\infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{e^{- x}}{x}\right) = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{e^{- x}}{x}\right) = e^{-1}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{e^{- x}}{x}\right) = e^{-1}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{e^{- x}}{x}\right) = -\infty$$
More at x→-oo
The graph