Question

The linear approximation to (1/(2-x)^(1/2) at x=0 is y=????
Help out with this problem??

Answer 1

\[f(x)=\frac{1}{\sqrt{2-x}},f(0)=\frac{1}{\sqrt{2}}\]
\[f'(x)=\frac{1}{2\sqrt{(2-x)^3}},f'(0)=\frac{1}{2\sqrt{8}}\]\]

Answer 2

equation for the line is
\[y-\frac{1}{\sqrt{2}}=\frac{1}{4\sqrt{2}}x\] or
\[y=\frac{1}{4\sqrt{2}}x+\frac{1}{\sqrt{2}}\] feel free to rationalize the denominators