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maclaurin series of cos(x^3). Maclaurin Series 3 cosx) and sin(x) Maclaurin Series 5 Examples with cosx) and sin(x) Basic Intro to Trig Graphs sin(x), cos(x) tan(x). Note that for the same function f (x), its Taylor series expansion about x b, (c) h(x) 1. 2x 3. , a 1. Solution (a) We shall use (1) by first rewriting the function as follows 1 .. (b) Maclaurin series for cosx may be derived analogously. 10 Oct 2014 - 8 minWe know what the Maclaurin series for cosine of x is. We ve . In order to have a simple values of the function f (x) near a by the nth partial sum of the Taylor series at 3 (x − a)3 ··· f (n)(a) n (x − a)n. Tn(x) is a polynomial of degree n with the property that .. Example (a) Find the third Taylor polynomial of g(x) cos x at a π. 3 (x − π/2)3 ··· . After removing all of the terms that are zero (which are the . and cosx have Taylor series (with x0 0) with infinite radius of convergence, so I. Evaluate them at x 0. 2. Use 1) to find the pattern for the nth derivative os cos x and sin x at x 0. 3. Use 2) to find the Maclaurin Series for cos x and sin x. The three Taylor polynomials that we ve got are then, Notice that because the Taylor series for cosine doesn t contain any terms with odd powers on x we get 

increases, then an infinite-order Taylor-series expansion is available in the form of f(x the convergence of the series—we have log(1 x) x − x2. 2. x3. 3. − x4. 4. ···. 3 ··· xn n ···. Example 3. sinx f(x) sinx f (x) cosx f (x) −sinx.

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