11. Suppose f and g are C" functions with Taylor expansions denoted Ta(f, xo, x) and Tn(g, xo, x). Prove that T,(f, xo, x)+ T,(9, x0, x) is the Taylor expansion of f +g at to. 12. Under the same...

Could we answer #12?

Extracted text: 11. Suppose f and g are C" functions with Taylor expansions denoted Ta(f, xo, x) and Tn(g, xo, x). Prove that T,(f, xo, x)+ T,(9, x0, x) is the Taylor expansion of f +g at to. 12. Under the same hypotheses as exercise 11, show that the Taylor expansion of f.g at 1o is obtained by taking T,(f, ¤o, x)T, (9, xo, x) and retaining only the powers of (x – ro) up to n.