Consider the following function.

Question

f(x) = sqrt(x) a = 4, n = 2, 4 ≤ x ≤ 4.5

 

Use Taylor's Inequality to estimate the accuracy of the approximation f(x) ≈ Tn(x) when x lies in the given interval.

 

 

R(2)(x) <=

Answer 1

Using Taylor’s inequality for f(x) = rad(x) around a=4 with n=2 on [4, 4.5]:

R2(x) 《 0.0.000244

So the error in the approximation f()~T2(x) is at most 0.000244.