Question

Obtain a four-term Taylor polynomial approximation valid near x=,0 for each (1+x)^-1/3. Estimate the range of x over which three term polynomials will give two decimal accuracy

Answer 1

Given, expression is...

f(x)=(1+x)^-1/3

On expanding the expression, we get the four term Taylor polynomial.

f(x)=1 -1/3*x+ 2/9*x^{2 _}14/81*x³

^{Range. i.e. Range of convergence of x is |x|<1}