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

Given function is fx=lnx We have to expand fx=lnx in power of x-1using Taylor series. The Taylor…

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) = AV (x) = Step 3: Let a =1 (From x-1, where a =1) f (1) = f' (1) = f" (1) = AV (1) = Step 4: Recall Taylor's Series and substitute values of f(0), f'(0), r0) .. f'(a)(x=a), ["(a)(x-a)² , "(a)(x=a)', 1! f"(a)(x=a)" f(x) = f (a) + +.+ 2! 3! n! f(x) = Step 5: Try to represent it in summation. f(x) = sin (x) = Eo( Step 6: Evaluate In 1.2. Using the series, let x= 1.2. Use your caleulator for checkir f(1.2) = In (1.2) =

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) = AV (x) = Step 3: Let a =1 (From x-1, where a =1) f (1) = f' (1) = f" (1) = AV (1) = Step 4: Recall Taylor's Series and substitute values of f(0), f'(0), r0) .. f'(a)(x=a), ["(a)(x-a)² , "(a)(x=a)', 1! f"(a)(x=a)" f(x) = f (a) + +.+ 2! 3! n! f(x) = Step 5: Try to represent it in summation. f(x) = sin (x) = Eo( Step 6: Evaluate In 1.2. Using the series, let x= 1.2. Use your caleulator for checkir f(1.2) = In (1.2) =

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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Question

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) =
fV (x) =
Step 3: Let a = 1 (From x-1, where a =1)
f (1) =
f' (1) =
= (1) ייr
fV (1) =
Step 4: Recall Taylor's Series and substitute values of f(0), f (0), r'(0) ..
f'(a)(x=a), f"(a)(x-a)² f"(a)(x=a)³
1!
f"(a)(x-a)"
f(x) = f (a) +
+...+
2!
3!
n !
f(x) =
Step 5: Try to represent it in summation.
f(x) = sin (x) = Eo()
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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