What is the limit as h approaches 0 of (2/(1+h)-2)/h ?

The limit as h approaches 0 of (2/(1+h)-2)/h is -2

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limit as h approaches 0 of (2/(1+h)-2)/h

h \to 0 lim (\frac{\frac{2}{1 + h} - 2}{h})

- 2

Solution steps

h \to 0 lim (\frac{\frac{2}{1 + h} - 2}{h})

Simplify

\frac{\frac{2}{1 + h} - 2}{h} : - \frac{2}{1 + h}

= h \to 0 lim (- \frac{2}{1 + h})

Plug in the value

h = 0

= - \frac{2}{1 + 0}

Simplify

= - 2

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What is the limit as h approaches 0 of (2/(1+h)-2)/h ?
The limit as h approaches 0 of (2/(1+h)-2)/h is -2