Unformatted text preview: at x = 1 (accurate upto at least 8 digits). Assuming that this results is “true”, ﬁnd the absolute errors for all the methods above. 3. (3 pts.) Consider the following numerical differentiation formula: f ( x ) ≈ α f ( x + h ) + β f ( x2 h ) γ h Find the appropriate values for α , β and γ for this formula to work (using Taylor series expansion). What is the order of your approximation? 4. (3 pts) Consider the following numerical differentiation formula: f ( x ) ≈f ( x + 2 h ) + 8 f ( x + h )8 f ( xh ) + f ( x2 h ) 12 h Prove that this is a valid formula (using Taylor’s expansion) and ﬁnd its order. 1 Note that x is in radians, that is, sin ( 2 π ) = 1. 1...
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 Fall '10
 caner
 Exponential Function, Derivative, Taylor Series, Natural logarithm, Taylor series expansion, numerical differentiation formula

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