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

# Find the limit of $\frac{x-8}{x^2-64}$ as $x$ approaches $8$

Go!
Symbolic 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 to the problem

$\frac{1}{16}$
Got another answer? Verify it here!

##  Step-by-step Solution 

How should I solve this problem?

• Choose an option
• Solve using L'Hôpital's rule
• Solve without using l'Hôpital
• 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
Can't find a method? Tell us so we can add it.
1

Factor the difference of squares $x^2-64$ as the product of two conjugated binomials

$\frac{x-8}{\left(x+8\right)\left(x-8\right)}$

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

$\frac{x-8}{\left(x+8\right)\left(x-8\right)}$

Learn how to solve limits by direct substitution problems step by step online. Find the limit of (x-8)/(x^2-64) as x approaches 8. Factor the difference of squares x^2-64 as the product of two conjugated binomials. Simplify the fraction . Evaluate the limit \lim_{x\to8}\left(\frac{1}{x+8}\right) by replacing all occurrences of x by 8. Add the values 8 and 8.

##  Final answer to the problem

$\frac{1}{16}$

##  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

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

###  Main Topic: Limits by Direct Substitution

Find limits of functions at a specific point by directly plugging the value into the function.
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "url": "https://www.snapxam.com/solver?p=%5Clim_%7Bx%5Cto8%7D%5Cleft%28%5Cfrac%7Bx-8%7D%7Bx%5E2-64%7D%5Cright%29", "fetch_time": 1721244668000000000, "content_mime_type": "text/html", "warc_filename": "crawl-data/CC-MAIN-2024-30/segments/1720763514801.32/warc/CC-MAIN-20240717182340-20240717212340-00810.warc.gz", "warc_record_offset": 849054172, "warc_record_length": 14480, "token_count": 802, "char_count": 2236, "score": 4.15625, "int_score": 4, "crawl": "CC-MAIN-2024-30", "snapshot_type": "latest", "language": "en", "language_score": 0.6743517518043518, "file_path": "/sailhome/yjruan/project/latent-lm/data/processed/finemath-4plus/finemath-4plus/train-00057-of-00064.parquet"}