Math, asked by sugyamsreehas, 3 months ago

The taylor's series expansion of f( x)in powers of (x+a) is​

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Answered by Anonymous
0

Answer:

A Taylor expansion of f around a allows to simply read off the the derivatives of arbitrary order at a. So its just a neat way to write the function which includes much information how this function behaves near that point.

This is useful for example when calculating limits of functions when x→a (l'Hospital rule).

As an example, if you have the polyomials f(x)=2(x−1)+3(x−1)2 and g(x)=x−1, then the limit

limx→1

f(x)

g(x)

= limx→1

2(x−1)+3(x−1)2

x−1

=2,

is easy to see. However, if we start with f(x)=3x2−4x+1, then calculating the limit is (still easy as the functions are easy, but) not trivial anymore.

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