If x is so small that x2 and higher powers of x can be neglected, then the approximate value of (1+(3/4) x)(1/2)(1-(2 x/3))-2 is

Question

If x is so small that x2 and higher powers of x can be neglected, then the approximate value of (1+(3/4) x)(1/2)(1-(2 x/3))-2 is (A) (41+24 x/41) (B) (41-24 x/41) (C) (24+41 x/24) (D) (24-41 x/24)

Tardigrade Admin · Accepted Answer

If x is so small that x2 and higher powers of x can be neglected, then ( l +x)n= 1 +n x So, (1+(3/4) x)1 / 2(1-(2/3) x)-2=(1+(3/8) x)(1+(4 x/3)) =1+(3/8) x+(4 x/3) [on neglecting the x2 term ] =(24+41 x/24)

Q. If $x$ is so small that $x^{2}$ and higher powers of $x$ can be neglected, then the approximate value of $(1 + \frac{3}{4} x)^{\frac{1}{2}} (1 - \frac{2 x}{3})^{- 2}$ is

$\frac{41 + 24 x}{41}$

$\frac{41 - 24 x}{41}$

$\frac{24 + 41 x}{24}$

$\frac{24 - 41 x}{24}$

Q. If x is so small that x2 and higher powers of x can be neglected, then the approximate value of (1+43​x)21​(1−32x​)−2 is

4141+24x​

4141−24x​

2424+41x​

2424−41x​

If x is so small that x2 and higher powers of x can be neglected, then (l+x)n=1+nx So, (1+43​x)1/2(1−32​x)−2=(1+83​x)(1+34x​) =1+83​x+34x​[on neglecting the x2 term ] =2424+41x​

Q. If $x$ is so small that $x^{2}$ and higher powers of $x$ can be neglected, then the approximate value of $(1 + \frac{3}{4} x)^{\frac{1}{2}} (1 - \frac{2 x}{3})^{- 2}$ is

$\frac{41 + 24 x}{41}$

$\frac{41 - 24 x}{41}$

$\frac{24 + 41 x}{24}$

$\frac{24 - 41 x}{24}$