Question

If \(|x|\) is so small that \(x^2\) and higher powers of \(x\) may be neglected, and hence \[ \frac{(8-3x)^{1/3}}{(2+3x)^3} \approx \frac{1}{a}(1+bx), \] then \(2ab=\) 

• A. \( -\frac{37}{2} \)
• B. \( -\frac{35}{2} \)
• C. \( -37 \)
• D. \( -35 \)

Hint:

Always ensure the constant term inside the parenthesis is \( 1 \) before applying the binomial approximation. If it is not, factor out the constant raised to the power first.

Answer 1

The Correct Option is C