Question

limit as x approaches 0 for

(cubed root(125 + x)) -5 / (x)

Answer 1

Apply L'Hospital Rule.

Answer 2

\[lim_{x\to0}\left(\frac{\sqrt[3]{125+x}-5}{x}\right)\]

We can apply the L'Hopital Rule.

\[lim_{x\to0}\frac{f(x)}{g(x)}=lim_{x\to0}\frac{f'(x)}{g'(x)}\]

then

\[lim_{x\to0}\left(\frac{1}{3*\sqrt[3]{(125+x)^2}}\right)\]

replace the approache

\[lim_{x\to0}\left(\frac{1}{3*\sqrt[3]{(125+0)^2}}\right)=\frac{1}{3*\sqrt[3]{125}}=\frac{1}{15}\]