💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

Verify the given linear approximation at $a = 0.$ Then determine the values of $x$ for which the linear approximation is accurate to within 0.1.$\ln (1 + x) \approx x$

$-0.3832<x<0.5162$

Discussion

You must be signed in to discuss.
Anna Marie V.

Campbell University

Kayleah T.

Harvey Mudd College

Kristen K.

University of Michigan - Ann Arbor

Michael J.

Idaho State University

Lectures

Join Bootcamp

Video Transcript

we know the first thing we're gonna be doing is the natural log of one plus ear, which is just the natural above one which we know zero. Therefore, we know that the derivative is one over one plus acts. Now, remember, the natural log of one plus axe is equivalent to axe. So then, if we're able to graft this, it would look something like this. And we know that X would be between negative 0.3832 and 0.5162

Anna Marie V.

Campbell University

Heather Z.

Oregon State University

Samuel H.

University of Nottingham

Boston College

Lectures

Join Bootcamp