Find the limit of $\left(x^2-3\right)e^x$ as $x$ approaches $\infty $

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Final answer to the problem

$\infty $
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Step-by-step Solution

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Evaluate the limit $\lim_{x\to\infty }\left(\left(x^2-3\right)e^x\right)$ by replacing all occurrences of $x$ by $\infty $

$\left(\infty ^2-3\right)\cdot e^{\infty }$

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

$\left(\infty ^2-3\right)\cdot e^{\infty }$

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Learn how to solve limits to infinity problems step by step online. Find the limit of (x^2-3)e^x as x approaches infinity. Evaluate the limit \lim_{x\to\infty }\left(\left(x^2-3\right)e^x\right) by replacing all occurrences of x by \infty . Infinity to the power of any positive number is equal to infinity, so \infty ^2=\infty. Apply a property of infinity: k^{\infty}=\infty if k>1. In this case k has the value e. Infinity plus any algebraic expression is equal to infinity.

Final answer to the problem

$\infty $

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Function Plot

Plotting: $\left(x^2-3\right)e^x$

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1
2
3
4
5
6
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

How to improve your answer:

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.

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