Question

Can anybody give me a general definition of a Maclaurin series and solve the exampleof f(x)=sin(2x)

Answer 1

Can you do \(h(x) = \sin(x)\)?

Answer 2

No I don't understand the series at all

Answer 3

Well, that's not very encouraging.

We just need a lot of derivatives. Show me the first four derivatives of your f(x) and we can talk.

Answer 4

Cos(2x)(2)

Answer 5

No?

Answer 6

That's one. Three more.

Answer 7

So is that all just the repetition of the derivative watt is the propose/final product

Answer 8

–4sin(2x)
–8cos(2x)
16Sin(2x)

Answer 9

That's about it. Now you just have to build it.

\(\dfrac{\sin(2\cdot 0)}{0!}x^{0} + \dfrac{2\cdot \cos(2\cdot 0)}{1!}x^{1} + \dfrac{-4\cdot \sin(2\cdot 0)}{2!}x^{2} + \dfrac{-8\cdot \cos(2\cdot 0)}{3!}x^{3} + ...\)

Eventually, you should notice two things:
1) All the terms with sin(0) simply drop out.
2) The series is alternating.

Answer 10

So the steps to constructing this is to fill in x with zero then put each derivative over increasing terrorists?

Answer 11

Darn auto correct mental factorial

Answer 12

Ment factorial

Answer 13

You evaluate each derivative at the desired point. In this case, x = 0 because we said "Maclaurin" in the Problem Statement.

Answer 14

Ok I think I have a decent idea thank you very much for your time and knowledge