FM5002-HW1-1.25.12

X y 0037 how many terms appear in the 6 th order

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Unformatted text preview: aclaurin approximation of a function of 9 variables? 2 This is equivalent to asking for the number of monomials of degree less than or equal to 6 on 9 variables, 69 which is just 5005. 9 0037 3. Find the second o rder Maclaurin approximation , q x, y , with respect to x, y t o the expression g x, y t an e2 x y 2 x y2 4 cos x 8 x. We compute : gx 0, y 0 g 8 x 4 2 y2 2 2x y 4xy Sec x 2 4 Cos x 4 4y y x g 2x y 2 , 8 Sec 1 2. y x 0, y 0 2x y Sec 2x y 2 8 4x 2y Sec 2x y 2 Tan 2 2x y Sec 2x y 2 4x 2y 4 Sec 2x y 2 Tan 4x 2x y Sec 2x y 2 2 4x 2y Sec 2x y 2 Tan 2x y Therefore, the second order Maclaurin approximation is 4 2 Sec 1 2. x 0, y 0 2x y 2x y , , 4 Sec 1 2 8 Sec 1 2 Tan 1 0037 4. Let f x, y x2 2 2 Sec 1 2 , 4 g 4 x2 8 Sec 1 2 Tan 1 . 2 Sec 1 2 4 Sec 1 2 Tan 1 . x 0, y 0 g y2 4 Sec 1 2 x 0, y 0 g xy 2 g 2 4 Sin x , 2 g xy g 2x y 2 Sec 2 g 2 2 2x y 2 g y Tan 1 . Sec 1 2 2 Sec 1 2 Tan 1 . x 0, y 0 Tan 1 4 Sec 1 2 Tan 1 x y 8 2 Sec 1 2 x Sec 1 2 Sec 1 2 y 2 Sec 1 2 Tan 1 y2 2 . 3 4 FM5002− HW1− 1.25.12− 2...
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