Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (e^(3*x)-x-e^(2*x))/x^2
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Limit of (1-x^3+5*x^4)/(x+2*x^4)
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Limit of (7+5*x^6)/(1+x^2)
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Limit of (6+n)/(4+n)
- Sum of series:
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2^n
- Graphing y =:
- 2^n
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Identical expressions
- two ^n
- 2 to the power of n
- two to the power of n
- 2n
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Similar expressions
- 1+2^n-2^(-n)
- ((-1+n^2)/(3+n^2))^(n^2)
- (-2)^n*2^(-n)*(1+n)
Limit of the function 2^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
$$\lim_{n \to \infty} 2^{n} = \infty$$
$$\lim_{n \to 0^-} 2^{n} = 1$$
More at n→0 from the left
$$\lim_{n \to 0^+} 2^{n} = 1$$
More at n→0 from the right
$$\lim_{n \to 1^-} 2^{n} = 2$$
More at n→1 from the left
$$\lim_{n \to 1^+} 2^{n} = 2$$
More at n→1 from the right
$$\lim_{n \to -\infty} 2^{n} = 0$$
More at n→-oo
$$\lim_{n \to 0^-} 2^{n} = 1$$
More at n→0 from the left
$$\lim_{n \to 0^+} 2^{n} = 1$$
More at n→0 from the right
$$\lim_{n \to 1^-} 2^{n} = 2$$
More at n→1 from the left
$$\lim_{n \to 1^+} 2^{n} = 2$$
More at n→1 from the right
$$\lim_{n \to -\infty} 2^{n} = 0$$
More at n→-oo
The graph