Expression 12: Start sum from "n" equals 0 to "k" , end sum, StartFraction, "x" Superscript, left parenthesis, 2 times "n" plus 1 , right parenthesis , Baseline Over left parenthesis, 2 times "n" plus 1 , right parenthesis ! , EndFraction left parenthesis, negative 1 , right parenthesis Superscript, left parenthesis, "n" , right parenthesis , Baselinek∑n=0x2·n+12·n+1!−1n
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Expression 13: "k" equals 1k=1
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Expression 14:
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Taylor Series of Sin(x) about x = c
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Expression 16: Start sum from "n" equals 0 to "m" , end sum, left parenthesis, StartFraction, left parenthesis, "x" minus "c" , right parenthesis Superscript, left parenthesis, 4 "n" , right parenthesis , Baseline Over left parenthesis, 4 "n" , right parenthesis ! , EndFraction times sin left parenthesis, "c" , right parenthesis plus StartFraction, left parenthesis, "x" minus "c" , right parenthesis Superscript, left parenthesis, 4 "n" plus 1 , right parenthesis , Baseline Over left parenthesis, 4 "n" plus 1 , right parenthesis ! , EndFraction times cos left parenthesis, "c" , right parenthesis minus StartFraction, left parenthesis, "x" minus "c" , right parenthesis Superscript, left parenthesis, 4 "n" plus 2 , right parenthesis , Baseline Over left parenthesis, 4 "n" plus 2 , right parenthesis ! , EndFraction times sin left parenthesis, "c" , right parenthesis negative StartFraction, left parenthesis, "x" minus "c" , right parenthesis Superscript, left parenthesis, 4 "n" plus 3 , right parenthesis , Baseline Over left parenthesis, 4 "n" plus 3 , right parenthesis ! , EndFraction times cos left parenthesis, "c" , right parenthesis , right parenthesism∑n=0x−c4n4n!·sinc+x−c4n+14n+1!·cosc−x−c4n+24n+2!·sinc−x−c4n+34n+3!·cosc
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Expression 17: "c" equals 0c=0
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Expression 18: "m" equals 0m=0
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Expression 19: left parenthesis, "c" , sin left parenthesis, "c" , right parenthesis , right parenthesisc,sinc
