**Maclaurin Series**

**SOUND COMPLICATED???**

**ITS PROBABLY THE EASIEST THING IN FP3 IF YOU KNOW YOUR WAY AROUND DIFFERENTIATION!!!!**

**BASICALLY, MACLAURIN SAID THAT:**

**Where f(x) is a function we want to find an expansion for.**

**EASY EXAMPLE:**

**Q: Find the first 3 non-zero terms in the Maclaurin Expansion of f(x) = Sin x**

**Well f(x) = Sin x**

**So f(0) = Sin 0 = 0**

**f'(x) = Cos x**

**So f'(0) = Cos 0 = 1**

**f''(x) = -Sin x**

**So f''(0) = - Sin 0 = 0**

**f'''(x) = - Cos x**

**So f'''(0) = - Cos 0 = -1**

**f''''(x) = Sin x**

**So f''''(0) = Sin 0 = 0**

**f'''''(x) = Cos x**

**So f'''''(0) = Cos 0 = 1**

**WE HAVE NOW FOUND OUR 3 NON-ZERO TERMS!!!!!**

**AS A SUMMARY:**

**f(0) = 0**

**f'(0) = 1**

**f''(0) = 0**

**f'''(0) = -1**

**f''''(0) = 0**

**f'''''(0) = 1**

**MACLAURIN SERIES:**

**So:**

** **

**THEREFORE THE ANSWER IS :**

**NOW LETS CHECK OUR ANSWER.**

**USING A CALCULATOR, SIN 0.5 = 0.479425538**

**PLUGGING 0.5 INTO THE EXPANSION, WE GET 0.479427083**

**EASY, ISN'T IT?????????**

**ALL YOU NEED TO KNOW IS DIFFERENTIATION**

**PLEASE FEEL FREE TO LEAVE HARDER EXAMPLES AND/OR CORRECT ANY MISTAKES ON THIS PAGE**

## Comments (2)

## Jason said

at 1:25 pm on May 11, 2009

PLEASE LEAVE COMMENTS IF I MADE A MISTAKE :)

## Steph Richards said

at 7:44 pm on May 11, 2009

Thank you for your contribution Jason. It is REALLY appreciated!

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