Use a Taylor polynomial for of degree 3 for the function fx

Use a Taylor polynomial for of degree 3 for the function f(x) 0.9521 0.9644 0.9767 0.9452 = to approximate about c = 1

taylor polynomial is

f(x)=f(a)+(x-a)f\'(a)+(x-a)^2f\'\'(a)/2+(x-a)^3f\'\'\'(a)/6

now f(x)=sqrtx

f\'(x)=1/(2sqrtx)

f\'\'(x)=-1/4(x^3/2)

f\'\'\'(x)=3/8(x^5/2)

now

f(1)=1

f\'(1)=1/2

f\'\'(1)=-1/4

f\'\'\'(1)=3/8

hence

f(0.93)=1+(-1+0.93)*1/2+(-1/8)(-1+0.93)^2+3(-1+0.93)^3/48

=0.96436=0.9644(approx)

hence 2