Question

Find the linear approximation of f(x)=\ln x at x=1 and use it to estimate ln 1.42

Answer 1

interpret as
"find the equation of the line tangent to \(y=\ln(x)\) at the point \((1,0)\)

Answer 2

you got that? take the derivative, plug in 1 to get your slope, then find the equation of the line using the point slope formula
that is all

Answer 3

okay, so would the equation be y-0=1(x-1) ?

Answer 4

yeah or just \(y=x-1\)

Answer 5

how do you solve for ln 1.42? i plugged it into my calculator but its not the right answer

Answer 6

replace \(x\) by \(1.42\) and get \(.42\)

Answer 7

it is kind of a lousy approximation but that is what you were asked for

Answer 8

ohh, thank you for the help!