KCET · Maths · Limits
\(\lim _{x \rightarrow 1} \frac{x^4-\sqrt{x}}{\sqrt{x}-1}\) is
- A \(0\)
- B \(7\)
- C Does not exist
- D \(\frac{1}{2}\)
Answer & Solution
Correct Answer
(B) \(7\)
Step-by-step Solution
Detailed explanation
\(\begin{gathered}\lim _{x \rightarrow 1} \frac{x^4-\sqrt{x}}{\sqrt{x}-1}=\lim _{x \rightarrow 1} \frac{4 x^3-\frac{1}{2 \sqrt{x}}}{\frac{1}{2 \sqrt{x}}}=\lim _{x \rightarrow 1} \frac{\frac{8 x^3 \sqrt{x}-1}{2 \sqrt{4}}}{\frac{1}{2 \sqrt{x}}} \\ =7\end{gathered}\)
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