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80 24c 80 C = 24 Write the 80 as the product of 5 and a power of 2. Write the 24 as a factorial. What pattern do you notice?

80 24c 80 C = 24 Write the 80 as the product of 5 and a power of 2. Write the 24 as a factorial. What pattern do you notice?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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8. In Problem 4, you should have found that for the fourth derivative P" (0) to equal f (0), the value of c4 was given by 80 24c, = 80 > C4 = 24 Write the 80 as the product of 5 and a power of 2. Write the 24 as a factorial. What pattern do you notice? Additional info 4. Function f is also locally cubic and locally quartic at x = 0. Find equations for the cubic and quartic functions, P3(x) = Co + Cx + C2x² + C3x' and P, (x) Co + Cx + Cx² + C3x' + Cx*, that best fit f(x) at x = 0. For these equations, P3 (0) and P,(0) must equal f(0), and the first three derivatives (for P3) or the first four derivatives (for P4) must equal the corresponding derivatives of f at x = 0. How do the coefficients co, C, and c2 compare with those for the quadratic and linear functions in Problems 2 and 3?
Transcribed Image Text:8. In Problem 4, you should have found that for the fourth derivative P" (0) to equal f (0), the value of c4 was given by 80 24c, = 80 > C4 = 24 Write the 80 as the product of 5 and a power of 2. Write the 24 as a factorial. What pattern do you notice? Additional info 4. Function f is also locally cubic and locally quartic at x = 0. Find equations for the cubic and quartic functions, P3(x) = Co + Cx + C2x² + C3x' and P, (x) Co + Cx + Cx² + C3x' + Cx*, that best fit f(x) at x = 0. For these equations, P3 (0) and P,(0) must equal f(0), and the first three derivatives (for P3) or the first four derivatives (for P4) must equal the corresponding derivatives of f at x = 0. How do the coefficients co, C, and c2 compare with those for the quadratic and linear functions in Problems 2 and 3?
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