What is the limit as h approaches 0 of ((3-sqrt(9+h)))/h ?

The limit as h approaches 0 of ((3-sqrt(9+h)))/h is -1/6

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limit as h approaches 0 of ((3-sqrt(9+h)))/h

h \to 0 lim (\frac{( 3 - 9 + h )}{h})

- \frac{1}{6}

Decimal

- 0.16666 \dots

Solution steps

h \to 0 lim (\frac{3 - 9 + h}{h})

Rationalize numerator

\frac{3 - 9 + h}{h} : - \frac{1}{3 + h + 9}

= h \to 0 lim (- \frac{1}{3 + h + 9})

Plug in the value

h = 0

= - \frac{1}{3 + 0 + 9}

Simplify

- \frac{1}{3 + 0 + 9} : - \frac{1}{6}

= - \frac{1}{6}

What is the limit as h approaches 0 of ((3-sqrt(9+h)))/h ?
The limit as h approaches 0 of ((3-sqrt(9+h)))/h is -1/6