Module 5 : Linear and Quadratic Approximations, Error Estimates, Taylor's Theorem, Newton and Picard Methods
Lecture 14 : Taylor's Theorem [Section 14.1]
Thus, for ,
.
For example, for
Thus, for
14.1.4
Note:
For , the Taylor polynomial for is nothing but the linear approximation. For a function , which is times differentiable in , we can use the degree Taylor 's polynomial to approximate in a small interval around . We analyze this for in the next section.
, 
.
, the Taylor polynomial for 
is nothing but the linear approximation. For a function 
, which is 
times differentiable in 
, we can use the 
degree Taylor 's polynomial to approximate 
in a small interval around 
. We analyze this for 
in the next section. 
