Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (1+3*x)^(5/x)
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Limit of (-16+x^2+6*x)/(-2-5*x+3*x^2)
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Limit of (1+x)^(2/3)-(-1+x)^(2/3)
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Limit of e^(1+3*x)*(-1+x)
- Sum of series:
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3^(-n)
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Identical expressions
- three ^(-n)
- 3 to the power of ( minus n)
- three to the power of ( minus n)
- 3(-n)
- 3-n
- 3^-n
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Similar expressions
- x*3^(-n)*sin(3^n)
- 2*n*3^(-n)
- n*3^(-n)*sin(3^n)
- 3^(n)
- 3^(-n)*(1+n)
Limit of the function 3^(-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
$$\lim_{n \to \infty} 3^{- n} = 0$$
$$\lim_{n \to 0^-} 3^{- n} = 1$$
More at n→0 from the left
$$\lim_{n \to 0^+} 3^{- n} = 1$$
More at n→0 from the right
$$\lim_{n \to 1^-} 3^{- n} = \frac{1}{3}$$
More at n→1 from the left
$$\lim_{n \to 1^+} 3^{- n} = \frac{1}{3}$$
More at n→1 from the right
$$\lim_{n \to -\infty} 3^{- n} = \infty$$
More at n→-oo
$$\lim_{n \to 0^-} 3^{- n} = 1$$
More at n→0 from the left
$$\lim_{n \to 0^+} 3^{- n} = 1$$
More at n→0 from the right
$$\lim_{n \to 1^-} 3^{- n} = \frac{1}{3}$$
More at n→1 from the left
$$\lim_{n \to 1^+} 3^{- n} = \frac{1}{3}$$
More at n→1 from the right
$$\lim_{n \to -\infty} 3^{- n} = \infty$$
More at n→-oo
The graph