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

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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

Mathematics
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I hate approximations >.<
Let me see.
k ty

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i just dont know where to start or what to do
hey anwara can u plz look at my problem too when u r done here
I think I am almost there :)
ty u so much i really appreciate it
Do you know how to find the Taylor expansion of a function?
can you please showme
Hmm, Do you have the formula of finding the Taylor expansion?
We're just looking for the third degree expansion, that's the first four terms.
okay my only question is what do i plug into x
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: \[\sqrt{1+1}=\sqrt{2}=1+{1 \over 2}-{1 \over 8}+{1 \over 16}={23 \over 16}\]
hey anwara can u plz look at my problem too when u r done here 14 minutes ago
okay so now what do i do with this value
Yeah sure rsaad2.
its on work done
Now this is the approximated value of sqrt(2), we're looking now for the error in this value.
Oh I don't really know what the bound on the magnitude of the error exactly is.
for the taylor series expansion did u use the binomial series to figure it out
now can u plz look at my problme plz
Well, I didn't. But, you could, it's actually easier to be found by the binomial series.
now can u plz look at my problem
so basically i would plug in sqrt of 1
Yep.
okay so u dont know how do the rest of the problem
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.
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
its under this topic Theorem 10.1 Lagrange Error Bound

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