## anonymous 5 years ago find the bound on the magnitude of the error if we approximate sqrt 2 using the taylor approximation of degree three for sqrt 1+x about x=0

1. anonymous

I hate approximations >.<

2. anonymous

Let me see.

3. anonymous

k ty

4. anonymous

i just dont know where to start or what to do

5. anonymous

hey anwara can u plz look at my problem too when u r done here

6. anonymous

I think I am almost there :)

7. anonymous

ty u so much i really appreciate it

8. anonymous

Do you know how to find the Taylor expansion of a function?

9. anonymous

can you please showme

10. anonymous

Hmm, Do you have the formula of finding the Taylor expansion?

11. anonymous

We're just looking for the third degree expansion, that's the first four terms.

12. anonymous

okay my only question is what do i plug into x

13. anonymous

That's good. So, we have the first four terms of the expansion: $\sqrt{1+x}=1+{x \over 2}-{x^2 \over 8}+{x^3 \over 16}+....$ We are looking for the approximation of sqrt(2), that's sqrt(1+1). So, we will plug x=1, and then we get: $\sqrt{1+1}=\sqrt{2}=1+{1 \over 2}-{1 \over 8}+{1 \over 16}={23 \over 16}$

14. anonymous

hey anwara can u plz look at my problem too when u r done here 14 minutes ago

15. anonymous

okay so now what do i do with this value

16. anonymous

17. anonymous

its on work done

18. anonymous

Now this is the approximated value of sqrt(2), we're looking now for the error in this value.

19. anonymous

Oh I don't really know what the bound on the magnitude of the error exactly is.

20. anonymous

for the taylor series expansion did u use the binomial series to figure it out

21. anonymous

now can u plz look at my problme plz

22. anonymous

Well, I didn't. But, you could, it's actually easier to be found by the binomial series.

23. anonymous

now can u plz look at my problem

24. anonymous

so basically i would plug in sqrt of 1

25. anonymous

Yep.

26. anonymous

okay so u dont know how do the rest of the problem

27. anonymous

Not really. I don't know what the bound on the magnitude of the error is. If you could provide me with a formula or any information regarding that, I might be able to help.

28. anonymous

if you click on this link you will see it http://math.jasonbhill.com/courses/fall-2010-math-2300-005/lectures/taylor-polynomial-error-bounds

29. anonymous

its under this topic Theorem 10.1 Lagrange Error Bound