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1995BC4

# 1995BC4 - 1995 — BC4 4 Let f be a function that has...

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Unformatted text preview: 1995 — BC4 4. Let f be a function that has derivatives of all orders for an real numbers. Assume f(1)= 3 , f’(1)= -—2 , f”(l) = 2 , and f”’(1) == 4 (3) Write the second-degree Taylor polynomial for f about x = l and use it to approximate f (O. 7). (b) Write the third-degree Taylor polynomial for f about x = 1 and use it to approximate f (1. 2) . (0) Write the second-degree Taylor poiynomiai for f ’. the derivative of f , about x = l and use it to appmximate f’(l.2). f”(a) (x "(1)2 + fm'(a) 2! 3! (x—a)3+ (a) f(X) = f(a) + f’(a)(x — a) + f.”(1) 2! f(x) = f(1)+f'(1)(x-1)+ (Jr-1)2 f(x) = 3 .... 2(x m1)+%(x «1): f(0.7) z 3+0.6+0.09~—»3.69 (b) f(x) = f(1)+ f’(l)(x — 1) + f”(1)(x_1)2+ ml) 3 22 32 (“1) f(x) = 3—2(x—l)+(x-l)2 “slimy f(1.2) = 3—0.4+0.04+%(0.003) = 2.6455 (C) f’(x) = —2 + 2(x - I) + 2(x —_1)2 f’(l.2) z —2 + 2(.2) + 2(2)2 1995 BC4 ...
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