Question

Find the linear approximation of f(x)=lnx at x=1 and use it to estimate ln(1.38).

Answer 1

$\bf f(x)=y=ln(x)\qquad \begin{cases} x=1\\ y=ln(1)\to y=0 \end{cases}\\\\ -----------------------------\\\\ \left. \cfrac{dy}{dx}=\cfrac{1}{x} \right|_{x=1}\implies 1\impliedby m \\\\\\ \textit{now, we know that } \begin{cases} x=1\\ y=0\\ m=1 \end{cases}\implies y-0=1(x-1)\implies y=x-1$

now, you're asked to use it when ln(1.38), which is just another way of saying x = 1.38

so set x = 1.38 and see what "y" is