Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
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Limit of (1+2*n)/(-1+3*n)
-
Limit of -2+x^3+6*x
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Limit of (2+x^2-3*x)/(4+x^2-5*x)
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Limit of (-15+x^2-2*x)/(-15-7*x+2*x^2)
- Graphing y =:
- exp(1/x)/x^2
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Identical expressions
- exp(one /x)/x^ two
- exponent of (1 divide by x) divide by x squared
- exponent of (one divide by x) divide by x to the power of two
- exp(1/x)/x2
- exp1/x/x2
- exp(1/x)/x²
- exp(1/x)/x to the power of 2
- exp1/x/x^2
- exp(1 divide by x) divide by x^2
Limit of the function exp(1/x)/x^2
The solution
You have entered
[src]
/ 1\
| -|
| x|
|e |
lim |--|
x->0+| 2|
\x /
$$\lim_{x \to 0^+}\left(\frac{e^{\frac{1}{x}}}{x^{2}}\right)$$
Limit(exp(1/x)/x^2, 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
$$\lim_{x \to 0^-}\left(\frac{e^{\frac{1}{x}}}{x^{2}}\right) = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{e^{\frac{1}{x}}}{x^{2}}\right) = \infty$$
$$\lim_{x \to \infty}\left(\frac{e^{\frac{1}{x}}}{x^{2}}\right) = 0$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{e^{\frac{1}{x}}}{x^{2}}\right) = e$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{e^{\frac{1}{x}}}{x^{2}}\right) = e$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{e^{\frac{1}{x}}}{x^{2}}\right) = 0$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{e^{\frac{1}{x}}}{x^{2}}\right) = \infty$$
$$\lim_{x \to \infty}\left(\frac{e^{\frac{1}{x}}}{x^{2}}\right) = 0$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{e^{\frac{1}{x}}}{x^{2}}\right) = e$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{e^{\frac{1}{x}}}{x^{2}}\right) = e$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{e^{\frac{1}{x}}}{x^{2}}\right) = 0$$
More at x→-oo
One‐sided limits
[src]
/ 1\
| -|
| x|
|e |
lim |--|
x->0+| 2|
\x /
$$\lim_{x \to 0^+}\left(\frac{e^{\frac{1}{x}}}{x^{2}}\right)$$
oo
$$\infty$$
= -2.12940793228068e-71
/ 1\
| -|
| x|
|e |
lim |--|
x->0-| 2|
\x /
$$\lim_{x \to 0^-}\left(\frac{e^{\frac{1}{x}}}{x^{2}}\right)$$
0
$$0$$
= 1.77320040811078e-76
= 1.77320040811078e-76
The graph