lim x→8 [tex] \frac{x - 8}{ \sqrt[3]{x} - 2} [/tex]

jawab

limit ( x-> 8)  (x- 8)/ (∛x - 2)

limit(x-> 8) (∛x - 2)( ∛(x²)  - 2∛ x + 4)/(∛x - 2)

limit (x-> 8) = ∛(x²) - 2∛x + 4
x= 8
limit = ∛(8²) - 2∛8 + 4
= ∛(4)³ - 2∛(2)³ + 4
= 4 - 4 + 4
= 4

[tex] \lim_{x \to8} \ \frac {x-8}{ \sqrt[3]{x}-2}\\ \lim_{x\to8}\ \frac {x-8}{x^{\frac {1}{3}}-2}\\ \\ \lim_{x\to8}\ \frac {(x^{\frac {1}{3}}-2)(x^{\frac {2}{3}}+2x^{\frac {1}{3}}+4)}{(x^{\frac {1}{3}}-2)}\\ \lim_{x\to8}\ \ x^{\frac {2}{3}}+2x^{\frac {1}{3}}+4\\ \lim_{x\to8}\ 8^{\frac {2}{3}}+2.8^{\frac {1}{3}}+4\\ \lim_{x\to8}\ 2^{3}^{.\frac {2}{3}}+2.2^{3}^{.\frac {1}{3}}+4\\ \lim_{x\to8}\ 2^2+2.2+4\\ \lim_{x\to8}\ 4+4+4\\ \lim_{x\to8}\ =12[/tex]