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Numerade Educator



Problem 9 Easy Difficulty

Use the definition of a Taylor series to find the first four nonzero terms of the series for $ f(x) $ centered at the given value of $ a. $

$ f(x) = \sin x, $ $ a = \pi/6 $




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Video Transcript

The problem is, use the definition of a tele Siri's tto find the first two four nine zero terms of the Siri's for half relax centered at is given one day. Mathematics is the go to sign axe a goto pie Where six So first, the first gym is half high over six. Which is he Control? Well, half and then I've prom is ICO took assign axe. So from high over six, it's the culture squire, it of three over, too. The second term is after prom pie over a six ham's X minus high over six, which is the cultural negative. Three over two times X minus pi over six. Second derivative is a connective sign axe. So after prom, prom at on PI over six is the Continental Behalf. Thirty Terms is a pram from high over six over two times X minus pi over six, which is called connective one. Force hands off. He's a squire house X minus pi over six square. Third. A derivative is a contra negative. Kasai Ajax. Soon the derivative high over six is a connective scarlet. Tow three over, too. So that fourth term of the series after prom, prom prom high over six over three factorial camps. Axe minus pi over six. The power of three, which is equally true. Negative route of three over two hands, one over three factorial times. Max Manus High over six to the power of three.