Mister Exam

Other calculators:

exp(1/x)/x
Limit of the function/ exp(1/x)/x

Limit of the function exp(1/x)/x

at →
v

For end points:

The graph:

from to

Piecewise:

The solution

You have entered [src] 
     /   1\
     | 1*-|
     |   x|
     |e   |
 lim |----|
x->0+\ x  /
$$\lim_{x \to 0^+}\left(\frac{e^{1 \cdot \frac{1}{x}}}{x}\right)$$ 
Limit(exp(1/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
Plot the graph
Rapid solution [src] 
oo
$$\infty$$
Expand and simplify
One‐sided limits [src] 
     /   1\
     | 1*-|
     |   x|
     |e   |
 lim |----|
x->0+\ x  /
$$\lim_{x \to 0^+}\left(\frac{e^{1 \cdot \frac{1}{x}}}{x}\right)$$ 
oo
$$\infty$$ 
= 2.25549168723769e-73
     /   1\
     | 1*-|
     |   x|
     |e   |
 lim |----|
x->0-\ x  /
$$\lim_{x \to 0^-}\left(\frac{e^{1 \cdot \frac{1}{x}}}{x}\right)$$ 
0
$$0$$ 
= 1.47337703210535e-78
= 1.47337703210535e-78
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-}\left(\frac{e^{1 \cdot \frac{1}{x}}}{x}\right) = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{e^{1 \cdot \frac{1}{x}}}{x}\right) = \infty$$
$$\lim_{x \to \infty}\left(\frac{e^{1 \cdot \frac{1}{x}}}{x}\right) = 0$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{e^{1 \cdot \frac{1}{x}}}{x}\right) = e$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{e^{1 \cdot \frac{1}{x}}}{x}\right) = e$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{e^{1 \cdot \frac{1}{x}}}{x}\right) = 0$$
More at x→-oo
Numerical answer [src] 
2.25549168723769e-73
2.25549168723769e-73
The graph
Limit of the function exp(1/x)/x
    © Mister Exam – Calculator