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 ▸Integrate with respect to x ) dy/dx= 6x^5
A curve C is mapped by the equation ( 1+x)(4-x). The curve intersects the x-axis at x = –1 and x = 4. A region R is bounded by C and the x-axis. Use calculus to find the exact area of R.
How do you find stationary points of an equation, eg. y=x^2+3x+2
Ignoring air resistance and assuming gravity to equal 9.81. If a ball of mass 1kg is dropped from a height of 100m, calculate it's final velocity before it hits the ground.