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

The limit as t approaches 0 of (sqrt(3+t)-sqrt(3-t))/t is 1/(sqrt(3))

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

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

\frac{1}{3}

Decimal

0.57735 \dots

Solution steps

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

Rationalize numerator

\frac{3 + t - 3 - t}{t} : \frac{2}{t + 3 + - t + 3}

= t \to 0 lim (\frac{2}{t + 3 + - t + 3})

Plug in the value

t = 0

= \frac{2}{0 + 3 + - 0 + 3}

Simplify

= \frac{1}{3}

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