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

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

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

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

- \frac{2}{h ^{3}}

Solution steps

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

Simplify

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

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

Plug in the value

x = 0

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

Simplify

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

= - \frac{2}{h ^{3}}

\int (x^{2} + 4) e^{- x} d x

\frac{d x}{d y} = x - x^{2}

\int t (t - 2) d t

t^{2} e^{4 t}

\frac{\partial}{\partial y} (x^{2} ln (y))

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