Find the Maclaurin series of f ( x) = sin x up to its fourth-order then write the Maclaurin series in sigma notation. Differentiate f ( x) = sin x four times in a row to find the expressions for f ′ ( x)

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First, take the function with its range to find the series for f (x). The Maclaurin formula is given by \ ( f (x)=∑k=0^∞ f^k (a)* x^k/ k! \) Find f^k (a) by evaluating the function derivative and adding

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The Maclaurin series of a function. f ( x) up to order n may be found using Series. [ f, x, 0, n] . It is a special case of Taylor series when x = 0. The Maclaurin series is given by. f ( x) = f ( x 0) + f ′ ( x

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f(4)(x) =sin(x) f ( 4) ( x) = s i n ( x) Notice that the derivatives repeat every four derivatives. Moreover, since the Maclaurin series is centered at zero, simply plug in zero into

x

Introduce the notion of Maclaurin series Cover the basic Maclaurin series (sine, cosine, exponential, logarithm) Indicate how to build new series from the basic series Examples: Find

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