Prove that if f(z) is an odd function, that is, f(-z) = –f(z) for all z E C, and f is analytic in a open disk containing 0, then the power series of f at zo 0 contains only odd terms.

Use the binomial series to find a Taylor polynomial of degree 3 for T3(x) = ) + Consider the following graph of f(x) 1.3+ 1.2- 1.1 + -0.9- 0.8- 0.7 0.6- 0.5 0.4 0.3 0.2 0.1 )x+ )x² + ) x ³ -1.5 -1.2 -0.9 -0.6 -0.3 M8 0.3 0.6 0.9 1.2 1.5 Identify the degree of the purple polynomial. 03 04 05 Identify the degree of the red polynomial. 03 04 05 Find the Maclaurin series of 4². Σ Σ n=0 = 1 1+ 4x 1+0.75x and two of its Taylor polynomials.