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 ▸

Identify the stationary points of f(x)=3x^3+2x^2+4 (by finding the first and second derivative) and determine their nature.


A rollercoaster stops at a point with GPE of 10kJ and then travels down a frictionless slope reaching a speed of 10 m/s at ground level. After this, what length of horizontal track (friction coefficient = 0.5) is needed to bring the rollercoaster to rest?


One important question type to be able to answer is integrating squared trig functions. like cos^2(x)


Find the second derivate d^2y/dx^2 when y = x^6 + sqrt(x).