Question

If $\frac{(1-3x{)}^{\frac{1}{2}}+(1-x{)}^{\frac{5}{3}}}{\sqrt{4-x}}$ is approximately equal to a + bx for small values of x, then (a, b) =

• A. (1, $\frac{35}{24}$)
• B. (1, - $\frac{35}{24}$)
• C. (2, $\frac{35}{12}$)
• D. (2, - $\frac{35}{12}$)

Answer 1

The correct option is B

(1, - $\frac{35}{24}$)

$\frac{(1-3x{)}^{1/2}+(1-x{)}^{5/3}}{2[1-\frac{x}{4}{]}^{1/2}}\frac{1}{2}\left[\right(1-\frac{3}{2}x)+(1-\frac{5x}{3}\left)\right](1+\frac{x}{8})\frac{1}{2}[2-\frac{19}{6}x]](1+\frac{x}{8})=\frac{1}{2}[2-(-\frac{1}{4}+\frac{19}{6}\left)x\right]=1-\frac{35}{24}x\therefore (a,b)=(1,-\frac{35}{24})$