What is the limit as t approaches 3 of (1/t-1/3)/(t-3) ?

The limit as t approaches 3 of (1/t-1/3)/(t-3) is -1/9

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limit as t approaches 3 of (1/t-1/3)/(t-3)

t \to 3 lim (\frac{\frac{1}{t} - \frac{1}{3}}{t - 3})

- \frac{1}{9}

Decimal Notation

- 0.11111 \dots

Solution steps

t \to 3 lim (\frac{\frac{1}{t} - \frac{1}{3}}{t - 3})

Simplify

\frac{\frac{1}{t} - \frac{1}{3}}{t - 3} : - \frac{1}{3 t}

= t \to 3 lim (- \frac{1}{3 t})

Plug in the value

t = 3

= - \frac{1}{3 \cdot 3}

Simplify

= - \frac{1}{9}

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What is the limit as t approaches 3 of (1/t-1/3)/(t-3) ?
The limit as t approaches 3 of (1/t-1/3)/(t-3) is -1/9