Find the limit of $\frac{x^3-9x}{x^2-3x}$ as $x$ approaches $3$

Step-by-step Solution

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Final answer to the problem

$6$
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Step-by-step Solution

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  • Solve using L'Hôpital's rule
  • Solve without using l'Hôpital
  • Solve using limit properties
  • Solve using direct substitution
  • Solve the limit using factorization
  • Solve the limit using rationalization
  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
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Factor the polynomial $x^3-9x$ by it's greatest common factor (GCF): $x$

$\lim_{x\to3}\left(\frac{x\left(x^2-9\right)}{x^2-3x}\right)$

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$\lim_{x\to3}\left(\frac{x\left(x^2-9\right)}{x^2-3x}\right)$

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Learn how to solve implicit differentiation problems step by step online. Find the limit of (x^3-9x)/(x^2-3x) as x approaches 3. Factor the polynomial x^3-9x by it's greatest common factor (GCF): x. Factor the polynomial x^2-3x by it's greatest common factor (GCF): x. Simplify the fraction \frac{x\left(x^2-9\right)}{x\left(x-3\right)} by x. Factor the difference of squares x^2-9 as the product of two conjugated binomials.

Final answer to the problem

$6$

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Function Plot

Plotting: $\frac{x^3-9x}{x^2-3x}$

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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: Implicit Differentiation

Implicit differentiation makes use of the chain rule to differentiate implicitly defined functions. For differentiating an implicit function y(x), defined by an equation R(x, y) = 0, it is not generally possible to solve it explicitly for y(x) and then differentiate. Instead, one can differentiate R(x, y) with respect to x and y and then solve a linear equation in dy/dx for getting explicitly the derivative in terms of x and y.

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