Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
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Limit of (2*x/(-3+2*x))^(3*x)
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Limit of (1-cos(8*x))/x^2
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Limit of (-sin(x)+tan(x))/sin(x)^3
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Limit of (-2+x^2-x)/(-2+x)
- Graphing y =:
- e^(1/x)
- Derivative of:
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e^(1/x)
- Integral of d{x}:
- e^(1/x)
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Identical expressions
- e^(one /x)
- e to the power of (1 divide by x)
- e to the power of (one divide by x)
- e(1/x)
- e1/x
- e^1/x
- e^(1 divide by x)
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Similar expressions
- (1+e^(1/x))/x
- -x-2*e^(1/x)+x*exp(1/x)
- x/(1+e^(1/x))
- e^(1/x)*x^3/(1+x)
Limit of the function e^(1/x)
The solution
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x ___ lim \/ E x->oo
$$\lim_{x \to \infty} e^{\frac{1}{x}}$$
Limit(E^(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
$$\lim_{x \to \infty} e^{\frac{1}{x}} = 1$$
$$\lim_{x \to 0^-} e^{\frac{1}{x}} = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+} e^{\frac{1}{x}} = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-} e^{\frac{1}{x}} = e$$
More at x→1 from the left
$$\lim_{x \to 1^+} e^{\frac{1}{x}} = e$$
More at x→1 from the right
$$\lim_{x \to -\infty} e^{\frac{1}{x}} = 1$$
More at x→-oo
$$\lim_{x \to 0^-} e^{\frac{1}{x}} = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+} e^{\frac{1}{x}} = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-} e^{\frac{1}{x}} = e$$
More at x→1 from the left
$$\lim_{x \to 1^+} e^{\frac{1}{x}} = e$$
More at x→1 from the right
$$\lim_{x \to -\infty} e^{\frac{1}{x}} = 1$$
More at x→-oo
The graph