Hi,

I was taking a practice exam from several years ago, and got tripped up by this question:

The polynomial p(x)=1+(1/2)(x-1)-(1/8)(x-1)^2 is used to approximate \sqrt(1.01). Which of the following most closely approximates the error \sqrt(1.01)-p(1.01)?

The answer is (1/16)x10^{-6}. But I do not know how they got this answer.

I would think that they want us to approximate p(1.01) by a tangent line approximation at x=1. But I don't know how to approximate the actual difference.

Thanks!