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hw4-sol - Assignment 4 Section 14.1 Problem 2 first using...

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Unformatted text preview: Assignment 4 Section 14.1 Problem 2: first using Δ? = 0.1 and Δ? = 0.1 , we have the estimates: ¡ ? 1,3 ¢ ≈ ¡ 1.1,3 ¢ − ¡ 1,3 ¢ 0.1 = 0.0470 − 0.0519 0.1 = − 0.0493 And ¡ ? 1,3 ¢ ≈ ¡ 1,3.1 ¢ − ¡ 1,3 ¢ 0.1 = 0.0153 − 0.0519 0.1 = − 0.3660 Now, using Δ? = 0.01 and Δ? = 0.01 , we have the estimates: ¡ ? 1,3 ¢ ≈ ¡ 1.01,3 ¢ − ¡ 1,3 ¢ 0.01 = 0.0514 − 0.0519 0.01 = − 0.0501 And ¡ ? 1,3 ¢ ≈ ¡ 1,3.01 ¢ − ¡ 1,3 ¢ 0.01 = 0.0483 − 0.0519 0.01 = − 0.3629 Problem 16: From the contour diagram, approximate the values of ¡ at nearby ?-values are ¡ 3,5 ¢ =10, ¡ 6.3,5 ¢ =8, ¡ 0.4,5 ¢ =12. Difference quotient approximations are ¡ ? 3,5 ¢ ≈ ¡ 6.3,5 ¢ − ¡ 3,5 ¢ 6.3 − 5 = − 0.61 ¡ ? 3,5 ¢ ≈ ¡ 0.4,5 ¢ − ¡ 3,5 ¢ 0.4 − 3 = − 0.77 Another reasonable approximation is obtained by averaging the two difference quotients: ¡ ?...
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hw4-sol - Assignment 4 Section 14.1 Problem 2 first using...

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