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

Step-by-step Solution

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Final Answer

$6$
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Step-by-step Solution

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Simplify $\sqrt{x^2}$ 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 $\frac{1}{2}$

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

Learn how to solve factor problems step by step online.

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

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Learn how to solve factor problems step by step online. Find the limit (x)->(3)lim((x^2-9)/(x-3)). Simplify \sqrt{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}{2}. Calculate the power \sqrt{9}. Simplify \sqrt{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}{2}. Calculate the power \sqrt{9}.

Final Answer

$6$

Exact Numeric Answer

$6$

Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Limits by Direct SubstitutionLimits by L'Hôpital's ruleLimits by FactoringLimits by Rationalizing

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Function Plot

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

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Answer Assistant

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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: Factor

Factor the expression.

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