Question

evaluate the limit
$lim_{b
ightarrow81}\frac{81 - b}{9-sqrt{b}}=square$.

Explanation:

Step1: Rationalize the denominator

Multiply the numerator and denominator by the conjugate of the denominator $9 + \sqrt{b}$.

$$
LATEXBLOCK0
$$

Since $(a - b)(a + b)=a^{2}-b^{2}$, the denominator is $81 - b$.

$$
LATEXBLOCK1
$$

Step2: Simplify the expression

Cancel out the common factor $81 - b$ (since $b
eq81$ when taking the limit).

$$
LATEXBLOCK2
$$

Step3: Evaluate the limit

Substitute $b = 81$ into the expression.

$$
LATEXBLOCK3
$$

Answer:

$18$