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# Find the limit $\lim_{x\to9}\left(\frac{\sqrt{x}-3}{x-9}\right)$

## Step-by-step Solution

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###  Solution

$\frac{1}{6}$
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##  Step-by-step Solution 

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Factor the difference of squares $x-9$ as the product of two conjugated binomials

$\frac{\sqrt{x}-3}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}$

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$\frac{\sqrt{x}-3}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}$

Learn how to solve problems step by step online. Find the limit (x)->(9)lim((x^1/2-3)/(x-9)). Factor the difference of squares x-9 as the product of two conjugated binomials. Simplify the fraction \frac{\sqrt{x}-3}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)} by \sqrt{x}-3. Evaluate the limit \lim_{x\to9}\left(\frac{1}{\sqrt{x}+3}\right) by replacing all occurrences of x by 9. Calculate the power \sqrt{9}.

$\frac{1}{6}$

$0.1667$

##  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

SnapXam A2

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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

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