:math: $_{k=0}^{} c_k (x-a)^k $ %%visits: 2 # taylor’s_series ## introduction ## intuition Error term can be written as $\frac{f^{(n+1)}(c}{(n+1)!}$ ## rigour ## exam clinic Remember standard expansions and then algebraically manipulate them to solve your equation.
So the general gist is to use a taylor expansion you already know of, and combine them accordingly. And to know when to stop (which just comes from practise I heard, plus it tends to 0 so anything that is bigger then x^2 in this case is going to go to zero) {{file:../figures/screenshot_20211202_125837.png}} ## examples and non-examples ## resources tags :math:calculus_1:calculus_2: