What is the limit as h approaches 0 of (sqrt(49+h)-7)/h ?

The limit as h approaches 0 of (sqrt(49+h)-7)/h is 1/14

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limit as h approaches 0 of (sqrt(49+h)-7)/h

h \to 0 lim (\frac{49 + h - 7}{h})

\frac{1}{14}

Decimal

0.07142 \dots

Solution steps

h \to 0 lim (\frac{49 + h - 7}{h})

Rationalize numerator

\frac{49 + h - 7}{h} : \frac{1}{h + 49 + 7}

= h \to 0 lim (\frac{1}{h + 49 + 7})

Plug in the value

h = 0

= \frac{1}{0 + 49 + 7}

Simplify

\frac{1}{0 + 49 + 7} : \frac{1}{14}

= \frac{1}{14}

What is the limit as h approaches 0 of (sqrt(49+h)-7)/h ?
The limit as h approaches 0 of (sqrt(49+h)-7)/h is 1/14