Real Analysis 46 | Application for Taylor's Theorem

[@jafetriosduran]

Your lectures are invaluable, thanks so much, such a great way to explain how to bound the error of the approximation

[@AMINE-dd1qy]

i have a test like in 20 min u keep saving me sir thank you so much ❤️

[@arturo3511]

Wouldn't it be a better approximation since we know that Rn(h) is negative for certain, we take xi = 1.2 and xi =1 which gives, 0.1822 - 1.92x10^-4 < log(1.2) < 0.1822 - 4x10^-4. This gives an approximation between 18.22 and 18.24 approximately instead of 18.31. Rn cant be positive so we know that values beyond 18.222 are not possible ?

[@brightsideofmaths]

Without checking your numbers, I can tell you that different/ better approximations are always possible. It wanted to show a standard approach here that works for a lot functions similarly.

[@lucaug10]

Taylor expansions are so nice

[@brightsideofmaths]

You can ask a physicist and she would say the same thing :)