What is the limit as x approaches a of ((\sqrt[3]{x})-\sqrt[3]{a})/(x^2-a^2) ?

The limit as x approaches a of ((\sqrt[3]{x})-\sqrt[3]{a})/(x^2-a^2) is 1/(6a^{5/3)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

limit as x approaches a of ((\sqrt[3]{x})-\sqrt[3]{a})/(x^2-a^2)

\frac{1}{6 a ^{\frac{5}{3}}}

Solution steps

Apply L'Hopital's Rule

: x \to a lim (\frac{\frac{1}{3 x ^{\frac{2}{3}}}}{2 x})

= x \to a lim (\frac{\frac{1}{3 x ^{\frac{2}{3}}}}{2 x})

Plug in the value

x = a

= \frac{\frac{1}{3 a ^{\frac{2}{3}}}}{2 a}

Simplify

\frac{\frac{1}{3 a ^{\frac{2}{3}}}}{2 a} : \frac{1}{6 a ^{\frac{5}{3}}}

= \frac{1}{6 a ^{\frac{5}{3}}}

\frac{\partial}{\partial z} (- z^{2})

\int \frac{6 x + 5}{( 9 x ^{2} + 15 x ) ^{5}} d x

\int_{4}^{8} t^{3} ln (5 t) d t

x y^{^{'}} + 2 y = 2 cos (x)

\frac{x ^{2} - 9 x + 1}{x ^{2} + 5}

What is the limit as x approaches a of ((\sqrt[3]{x})-\sqrt[3]{a})/(x^2-a^2) ?
The limit as x approaches a of ((\sqrt[3]{x})-\sqrt[3]{a})/(x^2-a^2) is 1/(6a^{5/3)}