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

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

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limit as y approaches x of (y^{2/3}-x^{2/3})/(y-x)

y \to x lim (\frac{y ^{\frac{2}{3}} - x ^{\frac{2}{3}}}{y - x})

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

Solution steps

y \to x lim (\frac{y ^{\frac{2}{3}} - x ^{\frac{2}{3}}}{y - x})

Apply L'Hopital's Rule

= y \to x lim \frac{\frac{2}{3 y ^{\frac{1}{3}}}}{1}

Plug in the value

y = x

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

Simplify

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

t an g e n t f (x) = x^{2}, at x = 5

\int 1 - cos (4 x) d x

\frac{d}{d x} (1 + x x)

d er i v a t i v e \frac{5}{2 x ^{6}}

x \to - 2 lim ((x + 1)^{7} (3 x^{2}))

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