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Taylor series the taylor series generated by f(x) at x=a is .. f(a) F(a) f(a)+ (x - a) + (x-( a)²+...... (x-a)n 1! 2! fn(a) n! Example/find the taylor series for f(x)=cos x at x=2π. Soltion// f(x)cos x. ƒ(2π) = 1 f(x) = -sinx. ƒ(2π) = 0 F(x) = - COS X. F(2π) = =-1 The taylor series is 1 1+0- (x- -2)²+..... 2! Example/find the taylor series for f(x)= ½- at x=2. Soltion// 1 f(x) == ½ ½ ƒ(2) = 1/1 f(x) = 11. F(2) 2 1 7(x) = 23. 7(2) = 1/13 - 11 = 8 4 = 44 The taylor series is 1 1 (x-2)+ 2 4 * 1! 1 4 * 2! (x − 2)²+..... -

Taylor series the taylor series generated by f(x) at x=a is .. f(a) F(a) f(a)+ (x - a) + (x-( a)²+...... (x-a)n 1! 2! fn(a) n! Example/find the taylor series for f(x)=cos x at x=2π. Soltion// f(x)cos x. ƒ(2π) = 1 f(x) = -sinx. ƒ(2π) = 0 F(x) = - COS X. F(2π) = =-1 The taylor series is 1 1+0- (x- -2)²+..... 2! Example/find the taylor series for f(x)= ½- at x=2. Soltion// 1 f(x) == ½ ½ ƒ(2) = 1/1 f(x) = 11. F(2) 2 1 7(x) = 23. 7(2) = 1/13 - 11 = 8 4 = 44 The taylor series is 1 1 (x-2)+ 2 4 * 1! 1 4 * 2! (x − 2)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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Taylor series the taylor series generated by f(x) at x=a is .. f(a) F(a) f(a)+ (x - a) + (x-( a)²+...... (x-a)n 1! 2! fn(a) n! Example/find the taylor series for f(x)=cos x at x=2π. Soltion// f(x)cos x. ƒ(2π) = 1 f(x) = -sinx. ƒ(2π) = 0 F(x) = - COS X. F(2π) = =-1 The taylor series is 1 1+0- (x- -2)²+..... 2! Example/find the taylor series for f(x)= ½- at x=2. Soltion// 1 f(x) == ½ ½ ƒ(2) = 1/1 f(x) = 11. F(2) 2 1 7(x) = 23. 7(2) = 1/13 - 11 = 8 4 = 44 The taylor series is 1 1 (x-2)+ 2 4 * 1! 1 4 * 2! (x − 2)²+..... -
Transcribed Image Text:Taylor series the taylor series generated by f(x) at x=a is .. f(a) F(a) f(a)+ (x - a) + (x-( a)²+...... (x-a)n 1! 2! fn(a) n! Example/find the taylor series for f(x)=cos x at x=2π. Soltion// f(x)cos x. ƒ(2π) = 1 f(x) = -sinx. ƒ(2π) = 0 F(x) = - COS X. F(2π) = =-1 The taylor series is 1 1+0- (x- -2)²+..... 2! Example/find the taylor series for f(x)= ½- at x=2. Soltion// 1 f(x) == ½ ½ ƒ(2) = 1/1 f(x) = 11. F(2) 2 1 7(x) = 23. 7(2) = 1/13 - 11 = 8 4 = 44 The taylor series is 1 1 (x-2)+ 2 4 * 1! 1 4 * 2! (x − 2)²+..... -
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