Question

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

Answer 1

I hate approximations >.<

Answer 2

Let me see.

Answer 3

k ty

Answer 4

i just dont know where to start or what to do

Answer 5

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

Answer 6

I think I am almost there :)

Answer 7

ty u so much i really appreciate it

Answer 8

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

Answer 9

can you please showme

Answer 10

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

Answer 11

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

Answer 12

okay my only question is what do i plug into x

Answer 13

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:
\[\sqrt{1+1}=\sqrt{2}=1+{1 \over 2}-{1 \over 8}+{1 \over 16}={23 \over 16}\]

Answer 14

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

Answer 15

okay so now what do i do with this value

Answer 16

Yeah sure rsaad2.

Answer 17

its on work done

Answer 18

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

Answer 19

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

Answer 20

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

Answer 21

now can u plz look at my problme plz

Answer 22

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

Answer 23

now can u plz look at my problem

Answer 24

so basically i would plug in sqrt of 1

Answer 25

Yep.

Answer 26

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

Answer 27

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.

Answer 28

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

Answer 29

its under this topic Theorem 10.1 Lagrange Error Bound