What is the limit as x approaches 0 of (sqrt(x)-1)/(\sqrt[3]{x)-1} ?

The limit as x approaches 0 of (sqrt(x)-1)/(\sqrt[3]{x)-1} is 1

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limit as x approaches 0 of (sqrt(x)-1)/(\sqrt[3]{x)-1}

x \to 0 lim (\frac{x - 1}{3 x - 1})

1

Solution steps

x \to 0 lim (\frac{x - 1}{3 x - 1})

Plug in the value

x = 0

= \frac{0 - 1}{3 0 - 1}

Simplify

= 1

\frac{d}{d x} (\frac{7}{3} x^{3} - 2 x^{2} + 10)

\int \frac{12 x + 30}{( x ^{2} + 2 x - 8 )} d x

\frac{\partial}{\partial y} (x^{3} + 3 x^{2} y - y^{4})

y^{^{''}} - 0.2 y^{^{'}} + 0.01 y = 0, y (0) = 15, y^{^{'}} (0) = b

x d y - (2 x + 1) e^{- y} d x = 0

What is the limit as x approaches 0 of (sqrt(x)-1)/(\sqrt[3]{x)-1} ?
The limit as x approaches 0 of (sqrt(x)-1)/(\sqrt[3]{x)-1} is 1