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1998BC3 - 1998 BC—3 Let f be a function that has...

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Unformatted text preview: 1998: BC—3 Let f be a function that has derivatives of all orders for all real numbers. Assume f{0) = 5, f'(0) : —3, f”(0) ; 1. and f“'(0) = 4. (a) Write the third-degree Taylor polynomial for f about x ; O and use it to approximate f(0.2). (b) Write the fourth-degree Taylor polynomial for g, where g(x) = f(x2). about x = O. I (c) Write the third-degree Taylor polynomial for h, where h(x) = I f(t) dt, about x = 0. 0 (d) Let h be defined as in part (c). Given that f(1) = 3, either find the exact value of MD or explain why it cannot be determined. f"(0) x2 + f”’(0) 2! 3! (a) fix) szO) +f'(0)x + x3 f(x) 25—3x+%x2+—::—x3 69 110.2) :3 4.425 @ (b) g(x) eflxz) z s w 3x2 + if © to) he) = f ’ftodr : f ‘(s — 3t + lap; o o 2 z5t—33—t‘2+—1—t3 sz—Exzh-l-x‘a’ @ 2 6 o 2 6 (d) The exact value of h( 1) cannot be determined because f (r) is not defined for 0 < t < I; it is defined only for t = 0 and r = 1. © 1998 BC3 ...
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