Question
Find the indicated limit. \( \lim _{x \rightarrow 8} \sqrt{4 \mathrm{x-6}} \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. \( \lim _{x \rightarrow 8} \sqrt{4 \mathrm{x}-6}=\square \) (lype an exact answer, using radicals as needed.) B. The limit does not exist.
Ask by Vaughan Frank. in the United States
Jan 22,2025
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Tutor-Verified Answer
Answer
The limit is \( \sqrt{26} \).
Solution
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Beyond the Answer
To find the limit \( \lim _{x \rightarrow 8} \sqrt{4(x-6)} \), we first substitute \( x = 8 \) into the expression: \[ \sqrt{4(8-6)} = \sqrt{4 \cdot 2} = \sqrt{8} = 2\sqrt{2}. \] Thus, the correct answer is: A. \( \lim _{x \rightarrow 8} \sqrt{4(x-6)} = 2\sqrt{2} \).