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ƒ(a + x) = f(a) + Σo_ x² d(n)f(x) an)f(x) = f(a) + xƒ'(a) + —ƒ"(a) + ¹ƒ''(a) + ·· . =1 n! dxn x=a By using the Taylor series, calculate sin 47°. (Hint: sin(45°) = 2)

ƒ(a + x) = f(a) + Σo_ x² d(n)f(x) an)f(x) = f(a) + xƒ'(a) + —ƒ"(a) + ¹ƒ''(a) + ·· . =1 n! dxn x=a By using the Taylor series, calculate sin 47°. (Hint: sin(45°) = 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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help with all parts if quesion thanks

(b) The Taylor series of f(x) about x = a can be expressed as ƒ(a + x) = f(a) + Σ%=1 xn_d(n)f(x) | n! dxn x=a . =ƒ(a) + xƒ'(a) +ƒ"(a) +¼ƒ''(a) + •n=1 3! By using the Taylor series, calculate sin 47º. (Hint: sin(45°) = 2) (Round your final answer to four decimal places. You should show the complete procedure of your calculation).
Transcribed Image Text:(b) The Taylor series of f(x) about x = a can be expressed as ƒ(a + x) = f(a) + Σ%=1 xn_d(n)f(x) | n! dxn x=a . =ƒ(a) + xƒ'(a) +ƒ"(a) +¼ƒ''(a) + •n=1 3! By using the Taylor series, calculate sin 47º. (Hint: sin(45°) = 2) (Round your final answer to four decimal places. You should show the complete procedure of your calculation).
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