Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (2+n)/(1+n)
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Limit of (-1+e^(3*x)-3*x)/sin(2*x)^2
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Limit of (1+e^x)^(1/x)
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Limit of sqrt(1-x+4*x^2)-2*x
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Identical expressions
- (one +e^x)^(one /x)
- (1 plus e to the power of x) to the power of (1 divide by x)
- (one plus e to the power of x) to the power of (one divide by x)
- (1+ex)(1/x)
- 1+ex1/x
- 1+e^x^1/x
- (1+e^x)^(1 divide by x)
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Similar expressions
- (1-e^x)^(1/x)
Limit of the function (1+e^x)^(1/x)
The solution
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x / x
lim \/ 1 + E
x->oo
$$\lim_{x \to \infty} \left(e^{x} + 1\right)^{\frac{1}{x}}$$
Limit((1 + E^x)^(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
$$\lim_{x \to \infty} \left(e^{x} + 1\right)^{\frac{1}{x}} = e$$
$$\lim_{x \to 0^-} \left(e^{x} + 1\right)^{\frac{1}{x}} = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+} \left(e^{x} + 1\right)^{\frac{1}{x}} = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-} \left(e^{x} + 1\right)^{\frac{1}{x}} = 1 + e$$
More at x→1 from the left
$$\lim_{x \to 1^+} \left(e^{x} + 1\right)^{\frac{1}{x}} = 1 + e$$
More at x→1 from the right
$$\lim_{x \to -\infty} \left(e^{x} + 1\right)^{\frac{1}{x}} = 1$$
More at x→-oo
$$\lim_{x \to 0^-} \left(e^{x} + 1\right)^{\frac{1}{x}} = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+} \left(e^{x} + 1\right)^{\frac{1}{x}} = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-} \left(e^{x} + 1\right)^{\frac{1}{x}} = 1 + e$$
More at x→1 from the left
$$\lim_{x \to 1^+} \left(e^{x} + 1\right)^{\frac{1}{x}} = 1 + e$$
More at x→1 from the right
$$\lim_{x \to -\infty} \left(e^{x} + 1\right)^{\frac{1}{x}} = 1$$
More at x→-oo
The graph