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

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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}

(1 + x^{2})^{- \frac{3}{2}}

\frac{d}{d x} (\frac{x ^{2} + 2 x - 2}{( x + 1 ) ^{2}})

f (x) = \frac{7}{x}, x = 1, x = 41

x \to 3 + lim (\frac{6 x}{x ^{2} - 9})

t sin (t)

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