Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
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Limit of (-9+x^2)/(-3+x^2-2*x)
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Limit of (-1+cos(x))/x^2
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Limit of sin(17*x)/sin(12*x)
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Limit of (5+x)/(-5+x^2+4*x)
- Derivative of:
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e^x/x
- Integral of d{x}:
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e^x/x
- Graphing y =:
- e^x/x
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Identical expressions
- e^x/x
- e to the power of x divide by x
- ex/x
- e^x divide by x
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Similar expressions
- (x+e^x)/(x^3-5*x)
- (1+e^x-x*e^x)/x
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What you mean?
- e^x/x
- e^(x/x)
- e^(x/x)
You entered:
e^x/x
What you mean?
Limit of the function e^x/x
The solution
You have entered
[src]
/ x\
|e |
lim |--|
x->0+\x /
$$\lim_{x \to 0^+}\left(\frac{e^{x}}{x}\right)$$
Limit(E^x/x, x, 0)
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
$$\lim_{x \to 0^-}\left(\frac{e^{x}}{x}\right) = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{e^{x}}{x}\right) = \infty$$
$$\lim_{x \to \infty}\left(\frac{e^{x}}{x}\right) = \infty$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{e^{x}}{x}\right) = e$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{e^{x}}{x}\right) = e$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{e^{x}}{x}\right) = 0$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{e^{x}}{x}\right) = \infty$$
$$\lim_{x \to \infty}\left(\frac{e^{x}}{x}\right) = \infty$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{e^{x}}{x}\right) = e$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{e^{x}}{x}\right) = e$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{e^{x}}{x}\right) = 0$$
More at x→-oo
One‐sided limits
[src]
/ x\
|e |
lim |--|
x->0+\x /
$$\lim_{x \to 0^+}\left(\frac{e^{x}}{x}\right)$$
oo
$$\infty$$
= 152.003318580017
/ x\
|e |
lim |--|
x->0-\x /
$$\lim_{x \to 0^-}\left(\frac{e^{x}}{x}\right)$$
-oo
$$-\infty$$
= -150.003303960743
= -150.003303960743
The graph