What is the limit as h approaches 0 of (sqrt(h+5)-sqrt(5))/h ?

The limit as h approaches 0 of (sqrt(h+5)-sqrt(5))/h is 1/(2sqrt(5))

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limit as h approaches 0 of (sqrt(h+5)-sqrt(5))/h

h \to 0 lim (\frac{h + 5 - 5}{h})

\frac{1}{2 5}

Decimal Notation

0.22360 \dots

Solution steps

h \to 0 lim (\frac{h + 5 - 5}{h})

Rationalize numerator

\frac{h + 5 - 5}{h} : \frac{1}{h + 5 + 5}

= h \to 0 lim (\frac{1}{h + 5 + 5})

Plug in the value

h = 0

= \frac{1}{0 + 5 + 5}

Simplify

= \frac{1}{2 5}

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What is the limit as h approaches 0 of (sqrt(h+5)-sqrt(5))/h ?
The limit as h approaches 0 of (sqrt(h+5)-sqrt(5))/h is 1/(2sqrt(5))