- #1
Poetria
- 267
- 42
Homework Statement
[/B]
Use the Taylor remainder theorem to give an expression of
##\sqrt 2 - P_3(1)##
P_3(x) - the degree 3 Taylor polynomial ##\sqrt {1+x}## in terms of c, where c is some number between 0 and 1
Find the maximum over the interval [0, 1] of the absolute value of the expression you entered above.2. The attempt at a solution
The fourth derivative of ##\sqrt {x}## :
##-\frac {15} {16*(x)^\frac 7 2}##
##\frac{-\frac {15} {16*(c)^\frac 7 2}} {4!}*x^4##
x=1
##\frac{-\frac {15} {16*(c)^\frac 7 2}} {4!}*1^4##
for c = 1 and x = 1
##|\sqrt 2 - P_3(1)| \leq |-5/128|##