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QuantumJG:
What is the difference between say:

Find the Taylor expansion of ex at x = 0 & Find the Taylor series for sinx at the point a = ?

Help my professor hasn't exactly explained what the Taylor series is.

/0:
Basically it's a polynomial approximation to a function. The more terms it has the more accurate it is.

http://en.wikipedia.org/wiki/Taylor_expansion
Wikipedia has a nice gif of a taylor expansion centred at 0.

If you centre your series at x = 0 then it will be most accurate at x = 0, and as it departs from that point it will start to diverge. Likewise, if you centre at , it will be very accurate there, but will diverge as you go out.

If you have a taylor series with an infinite number of terms, it doesn't matter where you centre it, since it will be exactly equal to the function within a reasonable domain. However if you want the infinite term expansion then its best to centre it at x = 0 otherwise you will be expanding an infinite number of brackets of the form

QuantumJG:
But what is the difference of a and x?

TrueTears:
a is where the function is centered at.

QuantumJG:
Let x . Graph the sequence:

.

How do I graph this?

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