Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of 7^(1/(-3+x))
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Limit of (3-3*x^2+4*x^4+6*x^3)/(2*x^2+7*x^4)
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Limit of ((5+4*x)/(-1+5*x))^(1+3*x)
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Limit of (-6-x^2-3*x+4*x^3)/(3-x^2+2*x^3)
- Derivative of:
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x*e^(1/x)
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Identical expressions
- x*e^(one /x)
- x multiply by e to the power of (1 divide by x)
- x multiply by e to the power of (one divide by x)
- x*e(1/x)
- x*e1/x
- xe^(1/x)
- xe(1/x)
- xe1/x
- xe^1/x
- x*e^(1 divide by x)
Limit of the function x*e^(1/x)
The solution
You have entered
[src]
/ x ___\ lim \x*\/ E / x->0+
$$\lim_{x \to 0^+}\left(e^{\frac{1}{x}} x\right)$$
Limit(x*E^(1/x), x, 0)
The graph
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-}\left(e^{\frac{1}{x}} x\right) = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(e^{\frac{1}{x}} x\right) = \infty$$
$$\lim_{x \to \infty}\left(e^{\frac{1}{x}} x\right) = \infty$$
More at x→oo
$$\lim_{x \to 1^-}\left(e^{\frac{1}{x}} x\right) = e$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(e^{\frac{1}{x}} x\right) = e$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(e^{\frac{1}{x}} x\right) = -\infty$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+}\left(e^{\frac{1}{x}} x\right) = \infty$$
$$\lim_{x \to \infty}\left(e^{\frac{1}{x}} x\right) = \infty$$
More at x→oo
$$\lim_{x \to 1^-}\left(e^{\frac{1}{x}} x\right) = e$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(e^{\frac{1}{x}} x\right) = e$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(e^{\frac{1}{x}} x\right) = -\infty$$
More at x→-oo
One‐sided limits
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/ x ___\ lim \x*\/ E / x->0+
$$\lim_{x \to 0^+}\left(e^{\frac{1}{x}} x\right)$$
oo
$$\infty$$
= 0.0657325076344887
/ x ___\ lim \x*\/ E / x->0-
$$\lim_{x \to 0^-}\left(e^{\frac{1}{x}} x\right)$$
0
$$0$$
= -2.6502391286206e-28
= -2.6502391286206e-28
The graph