(1) Determine whether each of the following statements is TRUE or FALSE. You do not have to explain. (a) If the Taylor p

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1 Determine Whether Each Of The Following Statements Is True Or False You Do Not Have To Explain A If The Taylor P 1 (158.33 KiB) Viewed 7 times

(1) Determine whether each of the following statements is TRUE or FALSE. You do not have to explain. (a) If the Taylor polynomial of degree 2 for f(x) near 0 is T₂(x) = 1 + x − x², then f(x) is increasing near x = 0. (b) If the Taylor polynomial of degree 2 for g(x) near 0 is T₂(x) = 1 + x², then g(x) has a local minimum at x = 0. (c) If the Taylor polynomial of degree 3 for h(x) near 0 is T3(x) = 1 + x − x³, then h(x) has an inflection point at x = 0. (d) If k(x) is a periodic function of period 27, then its second order Taylor poly- nomial at x = 0 equals its second order Taylor polynomial at x = 2π. (e) If l(x) is an odd function, then the Taylor series for near x = 0 has only terms of odd exponents.