Question

Express


`(4 - x) {}^{ (1)/(2) }`
in ascending power of x up to term x²

​

Answer 1

Explanation:

Remember:

`\boxed{(1+y)^{(1)/(2) }= 1+(y)/(2) -(y^2)/(2*4) +(1*3*y^3)/(2*4*6) +K\ with -1 < y \leq 1 }\\\\\\Let\ say\ 4-x=1+y\ or\ y=3-x\\\\\\(4-x)^{(1)/(2) }=1+(3-x)/(2) -((3-x)^2)/(2*4) +K\ with\ 2\leq x <4\\\\=(29)/(8) -(5x)/(4) +(x^2)/(8) +K\\`