Find the limit of $\frac{1-x\left(x^3-6x^2\right)^{-\frac{1}{3}}}{\left(x^3-6x^2\right)^{-\frac{1}{3}}}$ 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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1

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

$\lim_{x\to\infty }\left(\frac{1-x\left(x^3-6x^2\right)^{-\frac{1}{3}}}{\left(x^2\left(x-6\right)\right)^{-\frac{1}{3}}}\right)$

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$\lim_{x\to\infty }\left(\frac{1-x\left(x^3-6x^2\right)^{-\frac{1}{3}}}{\left(x^2\left(x-6\right)\right)^{-\frac{1}{3}}}\right)$

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Learn how to solve problems step by step online. Find the limit of (1-x(x^3-6x^2)^(-1/3))/((x^3-6x^2)^(-1/3)) as x approaches infinity. Factor the polynomial \left(x^3-6x^2\right) by it's greatest common factor (GCF): x^2. Factor the polynomial \left(x^3-6x^2\right) by it's greatest common factor (GCF): x^2. Evaluate the limit \lim_{x\to\infty }\left(\frac{1-x\left(x^2\left(x-6\right)\right)^{-\frac{1}{3}}}{\left(x^2\left(x-6\right)\right)^{-\frac{1}{3}}}\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.

Final answer to the problem

$\infty $

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Function Plot

Plotting: $\frac{1-x\left(x^3-6x^2\right)^{-\frac{1}{3}}}{\left(x^3-6x^2\right)^{-\frac{1}{3}}}$

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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

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