Question

Use differentials to approximate the value of ln(0.9)

Answer 1

\[\frac{d}{dx} ln x = \frac{1}{x}\]\[ln(1) = 0\]\[ln(1-.1) \approx ln(1) - .1(\frac{d}{dx}[lnx]|_{x=1})\]\[\approx0 - .1(\frac{1}{1}) \approx -.1\]

Answer 2

thank you!

Answer 3

You just need to recall what it means to be a differential. I honestly had to re-derive this one because I couldn't recall the exact formula or anything. Just had to go from the definition.