What is approximation? How is it related to linearization? What

>>8727707
>What is the formula for approximation?

Well it's normally a Taylor series. [eqn] \sum _{ n = 0 } ^{ \infty } \frac { f^{ (n) } (a) } { n! } ( x - a )^n [/math] where the [math] f ^{n} [/math] are the nth order derivatives evaluated at a.

>How is it related to linearization?
It's the first order term. So if we have something like [math] (1+x)^{1/2} [/math] then we can expand it as a Taylor series [eqn] (1+x)^{1/2} \approx 1 + \frac { x } { 2 } [/eqn] Which is the linear approximation at x=0.

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>>8727707
Best I got for ya. Read up on Limits.

>>8727921
I know how to the limits.

>>8727731
sum of what?

what is /math?

>>8728039
[eqn] \sum _{ n = 0 } ^{ \infty } \frac { f^{ (n) } (a) } { n! } ( x - a )^n [/eqn] Where a is the point about which you want your approximation.

>>8728041
To add on to this, the approximation is given by the difference between the value of this sum, and the value of the first so many terms (since you can't actually evaluate infinite terms without special methods), so linearization is taking the first two terms of this sum, and the error is the difference between the first two terms and the entire sum.