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

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

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

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

h^{2}

Solution steps

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

Plug in the value

x = 0

= \frac{( 0 + h ) ^{3} - 0}{h}

Simplify

\frac{( 0 + h ) ^{3} - 0}{h} : h^{2}

= h^{2}

\frac{d y}{d x} + y = e^{3 x}

\frac{\partial}{\partial x} (2 x^{3} - 54 x - 2 y^{2} - 12 y)

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

2 x^{5} - 11 x^{3}

\frac{\partial}{\partial x} (\frac{A ( x , v , t )}{( x - v t ) ^{2} + 1})

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