Question
30. . จงหาค่า \( \lim _{x \rightarrow 2} \sqrt{\frac{x^{2}+5}{x-1}} \)
Ask by Thornton Valdez. in Thailand
Mar 21,2025
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ค่าของ \( \lim _{x \rightarrow 2} \sqrt{\frac{x^{2}+5}{x-1}} \) คือ 3
Solution
Calculate or simplify the expression \( \lim_{x\rightarrow 2} \sqrt{\frac{x^{2}+5}{x-1}} \).
Evaluate the limit by following steps:
- step0: Evaluate the limit:
\(\lim _{x\rightarrow 2}\left(\sqrt{\frac{x^{2}+5}{x-1}}\right)\)
- step1: Rewrite the expression:
\(\sqrt{\lim _{x\rightarrow 2}\left(\frac{x^{2}+5}{x-1}\right)}\)
- step2: Calculate:
\(\sqrt{9}\)
- step3: Write in exponential form:
\(\sqrt{3^{2}}\)
- step4: Simplify the root:
\(3\)
ค่าของ \( \lim _{x \rightarrow 2} \sqrt{\frac{x^{2}+5}{x-1}} \) คือ 3
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เพื่อหาค่า \( \lim _{x \rightarrow 2} \sqrt{\frac{x^{2}+5}{x-1}} \) เราสามารถแทนค่า \( x = 2 \) ลงในนิพจน์ได้ เริ่มจากแทนค่า \( x \) ลงไปในเศษและส่วน: \[ \sqrt{\frac{2^{2}+5}{2-1}} = \sqrt{\frac{4+5}{1}} = \sqrt{\frac{9}{1}} = \sqrt{9} = 3 \] ดังนั้นค่า \( \lim _{x \rightarrow 2} \sqrt{\frac{x^{2}+5}{x-1}} \) คือ 3.
