Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of ((-1+x)/x)^(5*x)
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Limit of exp(-x)
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Limit of -11
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Limit of x^3-3*x^2
- Derivative of:
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exp(-x)
- Integral of d{x}:
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exp(-x)
- Graphing y =:
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exp(-x)
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Identical expressions
- exp(-x)
- exponent of ( minus x)
- exp-x
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Similar expressions
- exp(-x^2)
- exp(x)
- exp(-x^2)/x
Limit of the function exp(-x)
The solution
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-x lim e x->oo
$$\lim_{x \to \infty} e^{- x}$$
Limit(exp(-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
$$\lim_{x \to \infty} e^{- x} = 0$$
$$\lim_{x \to 0^-} e^{- x} = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+} e^{- x} = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-} e^{- x} = e^{-1}$$
More at x→1 from the left
$$\lim_{x \to 1^+} e^{- x} = e^{-1}$$
More at x→1 from the right
$$\lim_{x \to -\infty} e^{- x} = \infty$$
More at x→-oo
$$\lim_{x \to 0^-} e^{- x} = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+} e^{- x} = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-} e^{- x} = e^{-1}$$
More at x→1 from the left
$$\lim_{x \to 1^+} e^{- x} = e^{-1}$$
More at x→1 from the right
$$\lim_{x \to -\infty} e^{- x} = \infty$$
More at x→-oo
The graph