Question

express
$(4 - x) {}^{ \frac{1}{2} }$
in ascending power of x up to term x²

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Answer 1

Answer:

Step-by-step explanation:

Remember:

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