The faylor Series Byc. Numerical Differentiation Use forward and backward difference approximations of 0(h) and a centered. difference approximation of 0(h²) to estimate the first derivative of the function a f(x) = 25x²³ - 6x² + 7x-88 Evaluate the derivatives at x = 2 uring step size of h = 6.25. Compute your results with the true value of the derivatives f (x)? f ₁ ( ₂ ) = ? For h= 0.25 Xi -1 Xi xit) = 2-25 1.75 = 2 f(xi-1) = ? f (x₁) = ? f(xit|) = ?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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The faylor Series By C. Numerical Differentiation
Use forward and backward difference
approximations of 0(h) and a centered
difference approximation of 0(4²) to
estimate the first derivative of the function
f(x) = 2.5x²³ - 6x² + 7x=88
3
Evaluate the derivatives at x = 2 uring
step size of h = 6.25. Compute your results
with the true value of the derivatives
f'(x)
(X)= ?
f₁ (₂) = ?
2
For h= 0.25
-1
= 1.75
2
Xi
Xi
xit1 = 2-25
f(xi-1) = ?
f (x₁) = ?
f(xit|) = ?
Transcribed Image Text:The faylor Series By C. Numerical Differentiation Use forward and backward difference approximations of 0(h) and a centered difference approximation of 0(4²) to estimate the first derivative of the function f(x) = 2.5x²³ - 6x² + 7x=88 3 Evaluate the derivatives at x = 2 uring step size of h = 6.25. Compute your results with the true value of the derivatives f'(x) (X)= ? f₁ (₂) = ? 2 For h= 0.25 -1 = 1.75 2 Xi Xi xit1 = 2-25 f(xi-1) = ? f (x₁) = ? f(xit|) = ?
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