Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of ((3+x)^2+(3-x)^2)/((3-x)^2-(3+x)^2)
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Limit of (-1+x)/(-2+sqrt(3+x))
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Limit of (-x+tan(x))/x^3
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Limit of (-1+sqrt(x))/(-3+x)
- Derivative of:
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2^(1/x)
- Graphing y =:
- 2^(1/x)
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Identical expressions
- two ^(one /x)
- 2 to the power of (1 divide by x)
- two to the power of (one divide by x)
- 2(1/x)
- 21/x
- 2^1/x
- 2^(1 divide by x)
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Similar expressions
- (2+e^(x^2))^(1/x)
- (x^(-2))^(1/x)
Limit of the function 2^(1/x)
The solution
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x ___ lim \/ 2 x->oo
$$\lim_{x \to \infty} 2^{\frac{1}{x}}$$
Limit(2^(1/x), x, oo, dir='-')
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 x→0, -oo, +oo, 1
$$\lim_{x \to \infty} 2^{\frac{1}{x}} = 1$$
$$\lim_{x \to 0^-} 2^{\frac{1}{x}} = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+} 2^{\frac{1}{x}} = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-} 2^{\frac{1}{x}} = 2$$
More at x→1 from the left
$$\lim_{x \to 1^+} 2^{\frac{1}{x}} = 2$$
More at x→1 from the right
$$\lim_{x \to -\infty} 2^{\frac{1}{x}} = 1$$
More at x→-oo
$$\lim_{x \to 0^-} 2^{\frac{1}{x}} = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+} 2^{\frac{1}{x}} = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-} 2^{\frac{1}{x}} = 2$$
More at x→1 from the left
$$\lim_{x \to 1^+} 2^{\frac{1}{x}} = 2$$
More at x→1 from the right
$$\lim_{x \to -\infty} 2^{\frac{1}{x}} = 1$$
More at x→-oo
The graph