Calculus Examples

$lim_{x \to 3} \frac{t^{2 - 9}}{t - 3}$

Step 1

Evaluate the limit of $\frac{t^{2 - 9}}{t - 3}$ which is constant as $x$ approaches $3$ .

$\frac{t^{2 - 9}}{t - 3}$

Step 2

Simplify the answer.

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Step 2.1

Move $t^{2 - 9}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{(t - 3) t^{- (2 - 9)}}$

Step 2.2

Simplify the denominator.

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Step 2.2.1

Subtract $9$ from $2$ .

$\frac{1}{(t - 3) t^{- - 7}}$

Step 2.2.2

Multiply $- 1$ by $- 7$ .

$\frac{1}{(t - 3) t^{7}}$

Step 2.3

Reorder factors in $\frac{1}{(t - 3) t^{7}}$ .

$\frac{1}{t^{7} (t - 3)}$