Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of ((5+4*x)/(-1+5*x))^(1+3*x)
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Limit of 10+x^2+3*x^3+8*x
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Limit of (-16+2^x)/(-1+5*sqrt(x)*(5-x))
- Limit of x^2+a/(x^3-a^3)-x*(1+a)
- Integral of d{x}:
- e^(3/x)
- Derivative of:
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e^(3/x)
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Identical expressions
- e^(three /x)
- e to the power of (3 divide by x)
- e to the power of (three divide by x)
- e(3/x)
- e3/x
- e^3/x
- e^(3 divide by x)
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Similar expressions
- x*e^(3/x)/(1+x)
Limit of the function e^(3/x)
The solution
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3
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x
lim e
x->oo
$$\lim_{x \to \infty} e^{\frac{3}{x}}$$
Limit(E^(3/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
$$\lim_{x \to \infty} e^{\frac{3}{x}} = 1$$
$$\lim_{x \to 0^-} e^{\frac{3}{x}} = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+} e^{\frac{3}{x}} = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-} e^{\frac{3}{x}} = e^{3}$$
More at x→1 from the left
$$\lim_{x \to 1^+} e^{\frac{3}{x}} = e^{3}$$
More at x→1 from the right
$$\lim_{x \to -\infty} e^{\frac{3}{x}} = 1$$
More at x→-oo
$$\lim_{x \to 0^-} e^{\frac{3}{x}} = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+} e^{\frac{3}{x}} = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-} e^{\frac{3}{x}} = e^{3}$$
More at x→1 from the left
$$\lim_{x \to 1^+} e^{\frac{3}{x}} = e^{3}$$
More at x→1 from the right
$$\lim_{x \to -\infty} e^{\frac{3}{x}} = 1$$
More at x→-oo
The graph