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