Question

Evaluate limx->4 x(cube) - 64/x(square) - 16

Answer 1

Hey there!

$\lim_{(x \to 4)} ({ x^3 - [64/x^2 ]- 16 })$
= 4³ - 64/4² - 16
= 64 - 64/16 - 16
= 64 - 4 - 16
= 64 - 20
= 44 .

$\lim_{x \to 4} \frac { x^3 - 64} {x^2-16}$

= $\lim_{x \to 4} [\frac { (x - 4 ) (x^2 + 4x +16 } {(x+4)(x-4)} ]$
= $\lim_{x \to 4} \frac{ (x^2+4x+16) } { x+4}$
= 4²+4(4)+16/4+4
= 48/8
= 6 .

Hope helped!
Thanks!

Answer 2

x³ - 64 = (x - 4) (x² + 4x + 16)

x² - 16 = (x - 4) (x + 4)

⇔

lim (x³ - 64) / (x² - 16) =
x → 4

lim [ (x - 4) (x² + 4x + 16) ] / [ x - 4) (x + 4) ] =
x → 4

lim (x² + 4x + 16) / (x + 4) = (4² + 4 (4) + 16) / (4 + 4) = 48/8 = 6
x → 6