Question

Linear approximation:
f(x) = 1/(x^2+1) @ x = 1
approximate f(1.1)

Answer 1

:)

Answer 2

How did you derive f(x)?

Answer 3

\[
f(x)=\frac1{x^2+1}\\
f'(x)=\frac{d}{dx} (x^2+1)^{-1}=-2x(x^2+1)^{-2}=-\frac{2x}{x^4+2x^2+1}\\
f(1.1)\simeq f(1)+f'(1)[1.1-1]\\
\ \ \ \ \ \ \ \ \ =\frac12-\frac12(0.1)\\
\ \ \ \ \ \ \ \ \ =\frac{10-1}{20}\\
\ \ \ \ \ \ \ \ \ =\frac{9}{20}
\]
Sorry, fixed.