Find the limit of $12xe^{\frac{1}{x}}-12$ as $x$ approaches $\infty $

Step-by-step Solution

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Final answer to the problem

$12\left(c-f\right)$
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Step-by-step Solution

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  • Solve using L'Hôpital's rule
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  • Solve using limit properties
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  • Solve the limit using factorization
  • Solve the limit using rationalization
  • Integrate by partial fractions
  • Product of Binomials with Common Term
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Factor the polynomial $12xe^{\frac{1}{x}}-12$ by it's greatest common factor (GCF): $12$

$\lim_{x\to\infty }\left(12\left(xe^{\frac{1}{x}}-1\right)\right)$

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

$\lim_{x\to\infty }\left(12\left(xe^{\frac{1}{x}}-1\right)\right)$

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Learn how to solve limits to infinity problems step by step online. Find the limit of 12xe^(1/x)-12 as x approaches infinity. Factor the polynomial 12xe^{\frac{1}{x}}-12 by it's greatest common factor (GCF): 12. The limit of the product of a function and a constant is equal to the limit of the function, times the constant: \displaystyle \lim_{t\to 0}{\left(at\right)}=a\cdot\lim_{t\to 0}{\left(t\right)}. Applying rationalisation. Multiply and simplify the expression within the limit.

Final answer to the problem

$12\left(c-f\right)$

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Function Plot

Plotting: $12xe^{\frac{1}{x}}-12$

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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.

Used Formulas

See formulas (2)

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