What is the limit as x approaches 4 of (x^4-256)/(x^3-64) ?

The limit as x approaches 4 of (x^4-256)/(x^3-64) is 16/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

limit as x approaches 4 of (x^4-256)/(x^3-64)

x \to 4 lim (\frac{x ^{4} - 256}{x ^{3} - 64})

\frac{16}{3}

Decimal

5.33333 \dots

Solution steps

x \to 4 lim (\frac{x ^{4} - 256}{x ^{3} - 64})

Simplify

\frac{x ^{4} - 256}{x ^{3} - 64} : \frac{( x ^{2} + 16 ) ( x + 4 )}{x ^{2} + 4 x + 16}

= x \to 4 lim (\frac{( x ^{2} + 16 ) ( x + 4 )}{x ^{2} + 4 x + 16})

Plug in the value

x = 4

= \frac{( 4 ^{2} + 16 ) ( 4 + 4 )}{4 ^{2} + 4 \cdot 4 + 16}

Simplify

\frac{( 4 ^{2} + 16 ) ( 4 + 4 )}{4 ^{2} + 4 \cdot 4 + 16} : \frac{16}{3}

= \frac{16}{3}

What is the limit as x approaches 4 of (x^4-256)/(x^3-64) ?
The limit as x approaches 4 of (x^4-256)/(x^3-64) is 16/3