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exp(1/x)/x^2
Limit of the function/ exp(1/x)/x^2

Limit of the function exp(1/x)/x^2

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     / 1\
     | -|
     | x|
     |e |
 lim |--|
x->0+| 2|
     \x /
lim⁡x→0+(e1xx2)\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
02468-8-6-4-2-1010-20000002000000
Plot the graph
Other limits x→0, -oo, +oo, 1
lim⁡x→0−(e1xx2)=∞\lim_{x \to 0^-}\left(\frac{e^{\frac{1}{x}}}{x^{2}}\right) = \infty
More at x→0 from the left
lim⁡x→0+(e1xx2)=∞\lim_{x \to 0^+}\left(\frac{e^{\frac{1}{x}}}{x^{2}}\right) = \infty
lim⁡x→∞(e1xx2)=0\lim_{x \to \infty}\left(\frac{e^{\frac{1}{x}}}{x^{2}}\right) = 0
More at x→oo
lim⁡x→1−(e1xx2)=e\lim_{x \to 1^-}\left(\frac{e^{\frac{1}{x}}}{x^{2}}\right) = e
More at x→1 from the left
lim⁡x→1+(e1xx2)=e\lim_{x \to 1^+}\left(\frac{e^{\frac{1}{x}}}{x^{2}}\right) = e
More at x→1 from the right
lim⁡x→−∞(e1xx2)=0\lim_{x \to -\infty}\left(\frac{e^{\frac{1}{x}}}{x^{2}}\right) = 0
More at x→-oo
Rapid solution [src] 
oo
∞\infty
Expand and simplify
One‐sided limits [src] 
     / 1\
     | -|
     | x|
     |e |
 lim |--|
x->0+| 2|
     \x /
lim⁡x→0+(e1xx2)\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→0−(e1xx2)\lim_{x \to 0^-}\left(\frac{e^{\frac{1}{x}}}{x^{2}}\right) 
0
00 
= 1.77320040811078e-76
= 1.77320040811078e-76
Numerical answer [src] 
-2.12940793228068e-71
-2.12940793228068e-71
The graph
Limit of the function exp(1/x)/x^2
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