Question

For the function $e^{-x}$ the linear approximation around $x=2$ is

• A. $(3-x)e^{-2}$
• B. $1-x$
• C. $[3+2\sqrt{2}-(1+\sqrt{2}\left)x\right]e^{-2}$
• D. $e^{-2}$

Answer 1

The correct option is A $(3-x)e^{-2}$

$e^{-x}=e^{-2-x+2}$
$=e^{-2}{e}^{-(x-2)}$
$=e^{-2}[1-(x-2)+\frac{(x-2{)}^2}{2}]$
for linear approximation neglect $(x-2{)}^2$ and its higher powers
$=e^{-2}(1-x+2)$
$=e^{-2}(3-x)$