👉 Try now NerdPal! Our new math app on iOS and Android

Find the limit $\lim_{x\to5}\left(\frac{x^3-125}{x^2-25}\right)$

Step-by-step Solution

Go!
Math mode
Text mode
Go!
1
2
3
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

Final Answer

$\frac{15}{2}$
Got another answer? Verify it here!

Step-by-step Solution

Specify the solving method

1

Factor the difference of cubes: $a^3-b^3 = (a-b)(a^2+ab+b^2)$

$\lim_{x\to5}\left(\frac{\left(x- 125^{\frac{1}{3}}\right)\left(x^2+125^{\frac{1}{3}}x+125^{\frac{2}{3}}\right)}{x^2-25}\right)$

Learn how to solve limits by direct substitution problems step by step online.

$\lim_{x\to5}\left(\frac{\left(x- 125^{\frac{1}{3}}\right)\left(x^2+125^{\frac{1}{3}}x+125^{\frac{2}{3}}\right)}{x^2-25}\right)$

Unlock unlimited step-by-step solutions and much more!

Unlock the first 2 steps of this solution.

Learn how to solve limits by direct substitution problems step by step online. Find the limit (x)->(5)lim((x^3-125)/(x^2-25)). Factor the difference of cubes: a^3-b^3 = (a-b)(a^2+ab+b^2). Divide 1 by 3. Divide 1 by 3. Divide 2 by 3.

Final Answer

$\frac{15}{2}$

Exact Numeric Answer

$7.5$

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

Give us your feedback!

Function Plot

Plotting: $\frac{15}{2}$

SnapXam A2
Answer Assistant

beta
Got a different answer? Verify it!

Go!
1
2
3
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: Limits by Direct Substitution

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

Used Formulas

1. See formulas

Your Math & Physics Tutor. Powered by AI

Available 24/7, 365.

Complete step-by-step math solutions. No ads.

Includes multiple solving methods.

Support for more than 100 math topics.

Premium access on our iOS and Android apps as well.

20% discount on online tutoring.

Choose your Subscription plan:
Have a promo code?
Pay $39.97 USD securely with your payment method.
Please hold while your payment is being processed.
Create an Account