# Find the limit of $\frac{e^x}{x^2}$ as $x$ approaches $\infty$

## Step-by-step Solution

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$\infty$
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##  Step-by-step Solution 

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If we directly evaluate the limit $\lim_{x\to \infty }\left(\frac{e^x}{x^2}\right)$ as $x$ tends to $\infty$, we can see that it gives us an indeterminate form

$\frac{\infty }{\infty }$

Learn how to solve limits to infinity problems step by step online.

$\frac{\infty }{\infty }$

Learn how to solve limits to infinity problems step by step online. Find the limit of (e^x)/(x^2) as x approaches infinity. If we directly evaluate the limit \lim_{x\to \infty }\left(\frac{e^x}{x^2}\right) as x tends to \infty , we can see that it gives us an indeterminate form. We can solve this limit by applying L'H么pital's rule, which consists of calculating the derivative of both the numerator and the denominator separately. After deriving both the numerator and denominator, the limit results in. If we directly evaluate the limit \lim_{x\to \infty }\left(\frac{e^x}{2x}\right) as x tends to \infty , we can see that it gives us an indeterminate form.

$\infty$

##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Limits by Direct SubstitutionLimits by L'H么pital's ruleLimits by factoringLimits by rationalizing

SnapXam A2

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7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

### Main Topic: Limits to Infinity

The limit of a function f(x) when x tends to infinity is the value that the function takes as the value of x grows indefinitely.