$$\\lim_{x\\to16}\\frac{98 - 2x}{7 - \\sqrt{x}}$$
$$\\lim_{x\\to16}\\frac{98 - 2x}{7 - \\sqrt{x}}$$
Answer
Explanation:
Step1: Rationalize the denominator
Multiply the numerator and denominator by (7 + \sqrt{x}). [ \begin{align*} &\lim_{x\rightarrow16}\frac{(98 - 2x)(7+\sqrt{x})}{(7-\sqrt{x})(7 + \sqrt{x})}\ =&\lim_{x\rightarrow16}\frac{(98 - 2x)(7+\sqrt{x})}{49 - x} \end{align*} ] Factor out (2) from the numerator: (\lim_{x\rightarrow16}\frac{2(49 - x)(7+\sqrt{x})}{49 - x})
Step2: Simplify the expression
Cancel out the common factor ((49 - x)) (since (x\neq49) as (x\rightarrow16)): (\lim_{x\rightarrow16}2(7+\sqrt{x}))
Step3: Substitute (x = 16)
[ \begin{align*} &2(7+\sqrt{16})\ =&2(7 + 4)\ =&2\times11\ =&22 \end{align*} ]
Answer:
(22)