Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of ((1+x)^3-(-1+x)^3)/(1+x^2)
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Limit of (-2+sqrt(x))/(-4+x^2)
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Limit of sin(9*x)/(3*x)
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Limit of (2-2*x^3+7*x^4)/(3+x^4)
- Graphing y =:
- e^(-n)
- Integral of d{x}:
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e^(-n)
- Sum of series:
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e^(-n)
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Identical expressions
- e^(-n)
- e to the power of ( minus n)
- e(-n)
- e-n
- e^-n
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Similar expressions
- e^(n)
- cos(e^(-n)+1/n)
Limit of the function e^(-n)
The solution
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 n→0, -oo, +oo, 1
$$\lim_{n \to \infty} e^{- n} = 0$$
$$\lim_{n \to 0^-} e^{- n} = 1$$
More at n→0 from the left
$$\lim_{n \to 0^+} e^{- n} = 1$$
More at n→0 from the right
$$\lim_{n \to 1^-} e^{- n} = e^{-1}$$
More at n→1 from the left
$$\lim_{n \to 1^+} e^{- n} = e^{-1}$$
More at n→1 from the right
$$\lim_{n \to -\infty} e^{- n} = \infty$$
More at n→-oo
$$\lim_{n \to 0^-} e^{- n} = 1$$
More at n→0 from the left
$$\lim_{n \to 0^+} e^{- n} = 1$$
More at n→0 from the right
$$\lim_{n \to 1^-} e^{- n} = e^{-1}$$
More at n→1 from the left
$$\lim_{n \to 1^+} e^{- n} = e^{-1}$$
More at n→1 from the right
$$\lim_{n \to -\infty} e^{- n} = \infty$$
More at n→-oo
The graph