What is the limit as h approaches 0 of ((sqrt(16+h))-4)/h ?

The limit as h approaches 0 of ((sqrt(16+h))-4)/h is 1/8

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limit as h approaches 0 of ((sqrt(16+h))-4)/h

h \to 0 lim (\frac{( 16 + h ) - 4}{h})

\frac{1}{8}

Decimal

0.125

Solution steps

h \to 0 lim (\frac{16 + h - 4}{h})

Rationalize numerator

\frac{16 + h - 4}{h} : \frac{1}{h + 16 + 4}

= h \to 0 lim (\frac{1}{h + 16 + 4})

Plug in the value

h = 0

= \frac{1}{0 + 16 + 4}

Simplify

\frac{1}{0 + 16 + 4} : \frac{1}{8}

= \frac{1}{8}

What is the limit as h approaches 0 of ((sqrt(16+h))-4)/h ?
The limit as h approaches 0 of ((sqrt(16+h))-4)/h is 1/8