Find the limit of $\sqrt[3]{6x^2-x^3}+x$ as $x$ approaches $\infty $

Step-by-step Solution

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Final answer to the problem

$c-f$
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Step-by-step Solution

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Factor the polynomial $6x^2-x^3$ by it's greatest common factor (GCF): $x^2$

$\lim_{x\to\infty }\left(\sqrt[3]{x^2\left(6-x\right)}+x\right)$

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

$\lim_{x\to\infty }\left(\sqrt[3]{x^2\left(6-x\right)}+x\right)$

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Learn how to solve limits to infinity problems step by step online. Find the limit of (6x^2-x^3)^(1/3)+x as x approaches infinity. Factor the polynomial 6x^2-x^3 by it's greatest common factor (GCF): x^2. The power of a product is equal to the product of it's factors raised to the same power. Simplify \sqrt[3]{x^2} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 2 and n equals \frac{1}{3}. Applying rationalisation.

Final answer to the problem

$c-f$

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Function Plot

Plotting: $\sqrt[3]{6x^2-x^3}+x$

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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 (1)

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