Find the first three terms in the expansion of (4-x)^(-1/2) in ascending powers of x.

(4-x)-1/2 = (4 (1 - x/4))-1/2 = 1/2 (1 - x/4)-1/2 = 1/2 ( 1 + x/8 + 3x2/128 + ...) = 1/2 + x/16 + 3x2/256 + ...Therefore the first three terms are 1/2 + x/16 + 3x2/256

Related Maths A Level answers

All answers ▸

What is the gradient of the function f(x) = 2x^2 + 3x - 7 at the point where x = -2?


How do I integrate terms with sin^2(x) and cos^2(x) in them? For example integrate (1+sin(x))^2 with respect to x


Differentiate with respect to x: w=4x^2 + 3sin(2x)


Implicitly differentiate the following equation to find dy/dx in terms of x and y: 2x^2y + 2x + 4y – cos (piy) = 17