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# Find the limit of $\frac{x^2-25}{x-5}$ as $x$ approaches $5$

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sinh
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asinh
acosh
atanh
acoth
asech
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##  Final answer to the problem

$10$
Got another answer? Verify it here!

##  Step-by-step Solution 

How should I solve this problem?

• Solve using limit properties
• Solve using L'Hôpital's rule
• Solve without using l'Hôpital
• 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
• Integrate by substitution
Can't find a method? Tell us so we can add it.
1

Factor the difference of squares $x^2-25$ as the product of two conjugated binomials

$\frac{\left(x+5\right)\left(x-5\right)}{x-5}$
2

Simplify the fraction $\frac{\left(x+5\right)\left(x-5\right)}{x-5}$ by $x-5$

$x+5$
3

Evaluate the limit $\lim_{x\to5}\left(x+5\right)$ by replacing all occurrences of $x$ by $5$

$5+5$
4

Add the values $5$ and $5$

$10$

##  Final answer to the problem

$10$

##  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

SnapXam A2

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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

###  Main Topic: Limits by Direct Substitution

Find limits of functions at a specific point by directly plugging the value into the function.