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Step 3 f'(a) f(x) = f(a) + (x – a) + (x – a)? +! f"(a) f"(a) (x – a) + ... f (x) = Ei-o k=0 k! then

Step 3 f'(a) f(x) = f(a) + (x – a) + (x – a)? +! f"(a) f"(a) (x – a) + ... f (x) = Ei-o k=0 k! then

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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I can't see the final result of the step 3

f(4) (x) = (f(3) (x)' = (4x (2x² + 3) e²²)' = (16x* + 48x² + 12) e? = F (0))"" = 12 f(5) (x) = (f(4) (x)' = ((16x* + 48x? + 12) ez?)' = &x (4xª + 20x² + 15) er? » (f (0))(5) = 0 f(6) (x) = (F(6) (x)' = (&x (4x4 + 20x² + 15) e²)' = (64x° + 480x4 + 720x² + 120) e*² » (f (0))6 = 120 fM (x) = (F(6) (x))' = ((64x° + 480x4 + 720x² + 120) e*²)' = 16x (8x + 84x“ + 210x² + 105) ex² = (f (0))(7) = 0 f(8) (x) = (f(T) (x)' = (16x (8xº + 84x4 + 210x² + 105) e²²)' 32x? (8x° + 84x* +210x² + 105) e* + 16x (48x + 336x³ + 420x) e*² = + (128x + 1344x* + 3360x? + 1680) et? → (f (0))8) = 1680
Transcribed Image Text:f(4) (x) = (f(3) (x)' = (4x (2x² + 3) e²²)' = (16x* + 48x² + 12) e? = F (0))"" = 12 f(5) (x) = (f(4) (x)' = ((16x* + 48x? + 12) ez?)' = &x (4xª + 20x² + 15) er? » (f (0))(5) = 0 f(6) (x) = (F(6) (x)' = (&x (4x4 + 20x² + 15) e²)' = (64x° + 480x4 + 720x² + 120) e*² » (f (0))6 = 120 fM (x) = (F(6) (x))' = ((64x° + 480x4 + 720x² + 120) e*²)' = 16x (8x + 84x“ + 210x² + 105) ex² = (f (0))(7) = 0 f(8) (x) = (f(T) (x)' = (16x (8xº + 84x4 + 210x² + 105) e²²)' 32x? (8x° + 84x* +210x² + 105) e* + 16x (48x + 336x³ + 420x) e*² = + (128x + 1344x* + 3360x? + 1680) et? → (f (0))8) = 1680
→ Step 3 f"(a) 2(x – a) + '(x – a)² +x - a' + . f(K) (a) f'(a) (х — а) + 1! f(x) = f(a) + f (x) = Li=0 k! then Unexpected text node: 'f' Unexpected text node: 'f'
Transcribed Image Text:→ Step 3 f"(a) 2(x – a) + '(x – a)² +x - a' + . f(K) (a) f'(a) (х — а) + 1! f(x) = f(a) + f (x) = Li=0 k! then Unexpected text node: 'f' Unexpected text node: 'f'
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