Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (1+x^2+9*x)/(-5+2*x+7*x^2)
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Limit of (-8+x^2+2*x)/(-2+x)
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Limit of (4-x^2)/(3-x^2)
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Limit of (h-5*h^2+2*h^3)/(h^4-h^2)
- 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
- n*3^(-n)*sin(3^n)
- 2*n*3^(-n)
- 3^(n)
- 3^(-n)*x^3
- 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