Step-by-step Solution

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

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Final Answer

$10$
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Step-by-step Solution

Problem to solve:

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

Choose the solving method

1

The difference of the squares of two terms, divided by the difference of the same terms, is equal to the sum of the terms, in other words:

  • $\displaystyle\frac{a^2-b^2}{a-b}=a+b$
  • Where the value of $a$ is $x$
  • and the value of $b$ is $5$, therefore:
  • The fraction $\frac{x^2-25}{x-5}$ simplified equals $x+5$

$\lim_{x\to5}\left(x+5\right)$
2

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

$5+5$

Add the values $5$ and $5$

$10$
3

Simplifying, we get

$10$

Final Answer

$10$
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1
2
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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

Tips on how to improve your answer:

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

Main topic:

Limits by factoring

Time to solve it:

~ 0.03 s