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Problem: Taylor's Series Expand f(x) = In x in powers of (x-1) using Taylor's Series. Compute In 1.2. Step 1: Write the given function f(x) = Step 2: Get its derivative (at least until fourth derivative) f (x) = f'(x) = f''(x) = flv (x) = Step 3: Let a 1 (From x-1, where a -1) f(1) = f(1) = f(1) = Step 4: Recall Taylor's Series and substitute values of f(0), f(0), f'(0) .... f(x) = f(a) + ƒ'(a)(x−a) ¸ ƒ”(a)(x-a)²¸ ƒ˜(a)(x-a)³. f"(a)(x-a)" + +...+ 2! 31 72! f(x) = Step 5: Try to represent it in summation. f(x) = sin(x) = Σ²_o( ) Step 6: Evaluate in 1.2. Using the series, let x= 1.2. Use your calculator for checking. f(1.2) = In (1.2) =

Problem: Taylor's Series Expand f(x) = In x in powers of (x-1) using Taylor's Series. Compute In 1.2. Step 1: Write the given function f(x) = Step 2: Get its derivative (at least until fourth derivative) f (x) = f'(x) = f''(x) = flv (x) = Step 3: Let a 1 (From x-1, where a -1) f(1) = f(1) = f(1) = Step 4: Recall Taylor's Series and substitute values of f(0), f(0), f'(0) .... f(x) = f(a) + ƒ'(a)(x−a) ¸ ƒ”(a)(x-a)²¸ ƒ˜(a)(x-a)³. f"(a)(x-a)" + +...+ 2! 31 72! f(x) = Step 5: Try to represent it in summation. f(x) = sin(x) = Σ²_o( ) Step 6: Evaluate in 1.2. Using the series, let x= 1.2. Use your calculator for checking. f(1.2) = In (1.2) =

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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Problem: Taylor's Series Expand f(x) = In x in powers of (x-1) using Taylor's Series. Compute In 1.2. Step 1: Write the given function f(x) = Step 2: Get its derivative (at least until fourth derivative) f (x) = f''(x) = f''(x) = flv (x) = Step 3: Let a = 1 (From x-1, where a -1) f(1) = f(1) = fv (1) = Step 4: Recall Taylor's Series and substitute values of f(0), f(0), f'(0) .... f(x) = f (a) + f'(ª)(x−a)+ ƒ˜(a)(x-a)²¸ ƒ”(a)(x-a)³_ f"(a)(x-a)" +...+ 2! 3! 72! f(x) = Step 5: Try to represent it in summation. f(x) = sin(x) = {²,( ) Step 6: Evaluate In 1.2. Using the series, let x= 1.2. Use your calculator for checking. f(1.2) = In (1.2) =
Transcribed Image Text:Problem: Taylor's Series Expand f(x) = In x in powers of (x-1) using Taylor's Series. Compute In 1.2. Step 1: Write the given function f(x) = Step 2: Get its derivative (at least until fourth derivative) f (x) = f''(x) = f''(x) = flv (x) = Step 3: Let a = 1 (From x-1, where a -1) f(1) = f(1) = fv (1) = Step 4: Recall Taylor's Series and substitute values of f(0), f(0), f'(0) .... f(x) = f (a) + f'(ª)(x−a)+ ƒ˜(a)(x-a)²¸ ƒ”(a)(x-a)³_ f"(a)(x-a)" +...+ 2! 3! 72! f(x) = Step 5: Try to represent it in summation. f(x) = sin(x) = {²,( ) Step 6: Evaluate In 1.2. Using the series, let x= 1.2. Use your calculator for checking. f(1.2) = In (1.2) =
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