- #1
morenogabr
- 29
- 0
Homework Statement
(For power series about x=1) Using the error formula, show that [tex]\left|ln(1.5)-p_{3}(1.5)\right|\leq\frac{(0.5)^{4}}{4} [/tex]
Homework Equations
[tex]p_{3}(x) = x-1 - \frac{(x-1)^{2}}{2} + \frac{(x-1)^{3}}{3}[/tex]
[tex]\\\epsilon_{n}(x)=\frac{f^{n+1}(\xi)}{(n+1)!}(x-x_{o})^{n+1}\\where \xi lies between x_{o} and x[/tex]
The Attempt at a Solution
Im sure this is an easy one, but I can't think of any useful relationship between the difference |f(x)-p_3(x)| and that piece of the remainder function... any hints?
(excuse my latex crappiness)