AP EAMCET · Maths · Binomial Theorem
If \(|x|\) is so small that all terms containing \(x^2\) and higher powers of \(x\) can be neglected, then the approximate value of \(\frac{(3-5 x)^{\frac{1}{2}}}{(5-3 x)^2}\), when \(x=\frac{1}{\sqrt{363}}\), is
- A \(\frac{\sqrt{3}}{25}\)
- B \(\frac{1+30 \sqrt{3}}{75}\)
- C \(\frac{1-30 \sqrt{3}}{75}\)
- D \(\frac{1+30 \sqrt{3}}{750}\)
Answer & Solution
Correct Answer
(D) \(\frac{1+30 \sqrt{3}}{750}\)
Step-by-step Solution
Detailed explanation
\(\frac{(3-5 x)^{\frac{1}{2}}}{(5-3 x)^2} = 3^{\frac{1}{2}}(1-\frac{5}{3}x)^{\frac{1}{2}} \cdot 5^{-2}(1-\frac{3}{5}x)^{-2}\) \(\approx \sqrt{3}(1+\frac{1}{2}(-\frac{5}{3}x)) \cdot \frac{1}{25}(1+(-2)(-\frac{3}{5}x))\)…
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