## anonymous one year ago f(x) = e^(2x) + e^(−2x) Find an upper bound for the error in using the second degree Maclaurin polynomial of f to approximate f(0.5).

1. anonymous

I guess I have to use the Lagrange remainder formula, right? $E _{n}(x) = f(x) - T _{n}(x) =\frac{ f ^{(n+1)}(c) }{ (n+1)! }(x-a)^{(n+1)}$ Where c lies between x and a

2. anonymous

yes just plug the rest in

3. anonymous

So here a=0 right?

4. anonymous

i think so

5. anonymous

Is my 3rd derivative correct? I got... $8e ^{2x}-8e ^{-2x}$

6. anonymous

ya

7. anonymous

Cool, so then I get $E _{2}(0.5)=\frac{ e ^{2c} -e ^{-2c}}{ 6 }$

8. anonymous

yes! im surprised u asked for help cuz u get it

9. anonymous

Lol I don't know what to do next :D

10. anonymous

that is f(x)

11. anonymous

i see what u do now

12. anonymous

u have to

13. anonymous

replace x with .5

14. anonymous

What if I was trying to find the lower bound?