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Formla_Sheet

# Formla_Sheet - -1 f x 2 i ² Δ x 3[Simpson’s Rule If | f...

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Formula Sheet: MATH 138-W12-003 Midterm 2012 Trigonometric Identites: sin 2 x + cos 2 x = 1 tan 2 x + 1 = sec 2 x sin 2 x = 1 2 (1 - cos 2 x ) , cos 2 x = 1 2 (1 + cos 2 x ) . sin A cos B = 1 2 [sin( A - B ) + sin( A + B )] , sin A sin B = 1 2 [cos( A - B ) - cos( A + B )] , cos A cos B = 1 2 [cos( A - B ) + cos( A + B )] . cos( A ± B ) = cos A cos B sin A sin B sin( A ± B ) = sin A cos B ± cos A sin B Approximate (Numerical) Integration Formulas: Z b a f ( x ) dx L n = n X i =1 f ( x i - 1 x, [Left endpoint Rule] Z b a f ( x ) dx R n = n X i =1 f ( x i x, [Right endpoint Rule] Z b a f ( x ) dx M n = n X i =1 f ( x i x, with x i = 1 2 ( x i - 1 + x i ) [Midpoint Rule] Z b a f ( x ) dx T n = n X i =1 [ f ( x i - 1 ) + f ( x i )] Δ x 2 , [Trapezoidal Rule] Z b a f ( x ) dx S n = n/ 2 X i =1 f ( x 2( i - 1) ) + 4
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Unformatted text preview: -1 ) + f ( x 2 i ) ² Δ x 3 , [Simpson’s Rule] If | f 00 ( x ) | ≤ K for a ≤ x ≤ b then the errors for the Trapezoidal and Midpoints rules are | E T | ≤ K ( b-a ) 3 12 n 2 , | E M | ≤ K ( b-a ) 3 24 n 2 . If | f (4) ( x ) | ≤ K for a ≤ x ≤ b then the error for the Simpson’s rule is | E S | ≤ K ( b-a ) 5 180 n 4 . 1...
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