What is the limit as h approaches 0 of ((x+h)^{2/3}-(x^{2/3}))/h ?

The limit as h approaches 0 of ((x+h)^{2/3}-(x^{2/3}))/h is 2/(3x^{1/3)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

limit as h approaches 0 of ((x+h)^{2/3}-(x^{2/3}))/h

h \to 0 lim \frac{( x + h ) ^{\frac{2}{3}} - ( x ^{\frac{2}{3}} )}{h}

\frac{2}{3 x ^{\frac{1}{3}}}

Solution steps

h \to 0 lim (\frac{( x + h ) ^{\frac{2}{3}} - x ^{\frac{2}{3}}}{h})

Apply L'Hopital's Rule

: h \to 0 lim \frac{\frac{2}{3 ( h + x ) ^{\frac{1}{3}}}}{1}

= h \to 0 lim \frac{\frac{2}{3 ( h + x ) ^{\frac{1}{3}}}}{1}

Plug in the value

h = 0

= \frac{\frac{2}{3 ( 0 + x ) ^{\frac{1}{3}}}}{1}

Simplify

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

\int_{b}^{2 b} x^{5} d x

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

\int \frac{1}{3 x ^{2} + 5} d x

x^{2} y^{^{''}} - 7 x y^{^{'}} + 16 y = 0

y = - 3 x^{3} + x^{2} + 10 x, x \geq 0

What is the limit as h approaches 0 of ((x+h)^{2/3}-(x^{2/3}))/h ?
The limit as h approaches 0 of ((x+h)^{2/3}-(x^{2/3}))/h is 2/(3x^{1/3)}