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

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

If we directly evaluate the limit $\lim_{x\to 5}\left(\frac{x^2-25}{x-5}\right)$ as $x$ tends to $5$, we can see that it gives us an indeterminate form

$\frac{0}{0}$
2

We can solve this limit by applying L'H么pital's rule, which consists of calculating the derivative of both the numerator and the denominator separately

$\lim_{x\to 5}\left(\frac{\frac{d}{dx}\left(x^2-25\right)}{\frac{d}{dx}\left(x-5\right)}\right)$
3

After deriving both the numerator and denominator, the limit results in

$\lim_{x\to5}\left(2x\right)$
4

The limit of the product of a function and a constant is equal to the limit of the function, times the constant: $\displaystyle \lim_{t\to 0}{\left(at\right)}=a\cdot\lim_{t\to 0}{\left(t\right)}$

$2\lim_{x\to5}\left(x\right)$
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Evaluate the limit $\lim_{x\to5}\left(x\right)$ by replacing all occurrences of $x$ by $5$

$2\cdot 5$
6

Multiply $2$ times $5$

$10$

##  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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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.