BY neglecting `x^4` and higher powers of x show that `root(3)(x^2 + 64) - root(3)(x^2 +27) = 1 - 7/432 x^2`

If |x| is so small that x^2 and higher powers of x may be neglected show that ((4 - 7x )^(1//2))/((3 + 5x)^3) = 2/27 (1 - 47/8 x)

If |x| is so small that x^2 and higher powers of x may be neglected show that ((4 + 3x)^(1//2))/((3 - 2x)^2) = 2/9 + 41/108 x

If |x| is so small that x^2 and higher powers of x may be neglected show that (sqrt(4 -x )) (3 - x/2)^(-1) = 2/3 (1 +(x)/(24))

If |x| is so small that x^2 and higher powers of x many be neglected , prove that sqrt(9 - 2x) (3 + (4x)/(5))^(-1) = 1 - 17/45 x

If |x| is so small that x^2 and higher powers of x may be neglected show that ((8 + 3x)^(2//3))/((2 + 3x)sqrt(4 - 5x)) = 1 - (5x)/(8)

If |x| is so small that x^2 and higher powers of x may be neglected show that ((1 -2/3 x)^(3//2) . (32 + 5x)^(1//5))/((3 - x)^3) = 2/27 (1 + (x)/(32))

If |x| is so small that x^2 and higher powers of x many be neglected , prove that ((1 + 7x)^(2/3) . (1 - 4x)^(-2))/((4 + 7x)^(1/2)) = 1/2 (1 + 283/24 x)

Solve : root(4)(|x-3|^(x+1))=root(3)(|x-3|^(x-2)) .

sqrt(x^(-2)y^(3)) root(4)(root(3)(x^(2)))

Assuming x to be so small that x^2 and higher power of x can be neglected, prove that ((1+(3x)/4)^-4(16-3x)^(1/2))/(8+x)^(2/3) = 1-(305/96)x