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Unformatted text preview: (x) + cos (x) 2 2 f'(x) = 2*sin(x)*cos(x) 2 * cos(x) * sin(x) f(x) ~ f(0) + x*f'(0) + . .. ~ Taylor series Taylor series Taylor series: f(x) ~ f(c) + (xc)*f'(c) + (xc) *f''(c) +(xc) *f'''(c) + . .. ~ 2 3 3! 2! Taylor series f(x) = ln x at x = 1 f'(x) = 1/x = x1 f''(x) = x2 f'''(x) = 2x3 f(1) = 0 f'(1) = 1 f''(1) = 1 f'''(1) = 2 Taylor series f(x) = ln x at x = 1 f(1) = 0 f'(1) = 1 f''(1) = 1 f'''(1) = 2 f(x) = 0 + (x1) (x1) 2 + 2(x1) 3 2 3! 2 f(x) = 0 Taylor series Taylor series: f(x+h) ~ f(x) + h*f'(x) + h *f''(x) + h *f'''(x) + . .. ~ 2 3 3! 2!...
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 Spring '08
 MEYER
 Taylor Series, Natural logarithm

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