Expression 19: "y" equals left brace, negative pi less than or equal to "x" less than 0 : 1 , 0 less than or equal to "x" less than pi : "x" , right bracey=−π≤x<0:1,0≤x<π:x
19
Expression 20: "y" equals StartFraction, 2 plus pi Over 4 , EndFraction plus Start sum from "n" equals 1 to "N" , end sum, left bracket, left parenthesis, StartFraction, cos left parenthesis, "n" pi , right parenthesis minus 1 Over pi "n" squared , EndFraction , right parenthesis cos left parenthesis, "n" "x" , right parenthesis plus left parenthesis, StartFraction, left parenthesis, negative 1 , right parenthesis Superscript, "n" , Baseline minus 1 minus pi left parenthesis, negative 1 , right parenthesis Superscript, "n" , Baseline Over "n" pi , EndFraction , right parenthesis sin left parenthesis, "n" "x" , right parenthesis , right brackety=2+π4+N∑n=1cosnπ−1πn2cosnx+−1n−1−π−1nnπsinnx
20
Expression 21: "y" equals left brace, negative pi less than or equal to "x" less than negative StartFraction, pi Over 2 , EndFraction : 0 , negative StartFraction, pi Over 2 , EndFraction less than or equal to "x" less than StartFraction, pi Over 2 , EndFraction : 1 , StartFraction, pi Over 2 , EndFraction less than or equal to "x" less than pi : 0 , right bracey=−π≤x<−π2:0,−π2≤x<π2:1,π2≤x<π:0
21
Expression 22: "y" equals 1 half plus Start sum from "n" equals 1 to "N" , end sum, left bracket, StartFraction, 2sin left parenthesis, StartNestedFraction, "n" pi NestedOver 2 , EndNestedFraction , right parenthesis Over "n" pi , EndFraction cos left parenthesis, "n" "x" , right parenthesis , right brackety=12+N∑n=12sinnπ2nπcosnx
22
Expression 23: "y" equals left brace, negative 4 less than or equal to "t" less than 0 : 0 , 0 less than or equal to "t" less than 4 : 2 , right bracey=−4≤t<0:0,0≤t<4:2
23
Expression 24: "y" equals 1 plus Start sum from "n" equals 1 to "N" , end sum, StartFraction, 4 Over left parenthesis, 2 "n" minus 1 , right parenthesis pi , EndFraction sine left parenthesis, StartFraction, left parenthesis, 2 "n" minus 1 , right parenthesis pi "t" Over 4 , EndFraction , right parenthesisy=1+N∑n=142n−1πsin2n−1πt4
24
Expression 25: "y" equals left brace, negative 1 less than "x" less than 1 : 1 , negative 2 less than "x" less than negative 1 : 0 , 1 less than "x" less than 2 : 0 , right bracey=−1<x<1:1,−2<x<−1:0,1<x<2:0
25
Expression 26: "y" equals 1 half plus Start sum from "n" equals 1 to "N" , end sum, StartFraction, 2 Over "n" pi , EndFraction sine left parenthesis, StartFraction, "n" pi Over 2 , EndFraction , right parenthesis cosine left parenthesis, StartFraction, "n" pi "x" Over 2 , EndFraction , right parenthesisy=12+N∑n=12nπsinnπ2cosnπx2
26
Expression 27: "y" equals left brace, negative 1 less than "x" less than 1 , right brace "x"y=−1<x<1x
27
Expression 28: "y" equals Start sum from "n" equals 1 to "N" , end sum, minus StartFraction, 2 Over "n" pi , EndFraction cosine left parenthesis, "n" pi , right parenthesis sine left parenthesis, "n" pi "x" , right parenthesisy=N∑n=1−2nπcosnπsinnπx
28
Expression 29: "y" equals left brace, negative StartFraction, pi Over 2 , EndFraction less than "x" less than 0 : 1 , 0 less than "x" less than StartFraction, pi Over 2 , EndFraction : negative 1 , right bracey=−π2<x<0:1,0<x<π2:−1
29
Expression 30: Start sum from "n" equals 1 to "N" , end sum, StartFraction, 2 Over "n" pi , EndFraction left parenthesis, cos left parenthesis, "n" pi , right parenthesis minus 1 , right parenthesis sine left parenthesis, 2 "n" "x" , right parenthesisN∑n=12nπcosnπ−1sin2nx
30
Expression 31: "M" equals 13M=13
11
5050
31
Expression 32: "L" equals 1L=1
11
44
32
Expression 33: "y" equals left brace, negative "L" less than "x" less than "L" : "x" , right bracey=−L<x<L:x
33
Expression 34: Start sum from "n" equals 1 to "M" , end sum, minus StartFraction, 2 "L" Over "n" pi , EndFraction cosine left parenthesis, "n" pi , right parenthesis sine left parenthesis, StartFraction, "n" pi "x" Over "L" , EndFraction , right parenthesisM∑n=1−2LnπcosnπsinnπxL
34
Expression 35: "y" equals left brace, negative 2 less than "x" less than negative 1 : 1 , negative 1 less than "x" less than 1 : 3 , 1 less than "x" less than 2 : 1 , right bracey=−2<x<−1:1,−1<x<1:3,1<x<2:1
35
Expression 36: 2 plus Start sum from "n" equals 1 to "M" , end sum, StartFraction, 4 Over "n" pi , EndFraction sine left parenthesis, StartFraction, "n" pi Over 2 , EndFraction , right parenthesis cosine left parenthesis, StartFraction, "n" pi "x" Over 2 , EndFraction , right parenthesis2+M∑n=14nπsinnπ2cosnπx2
36
Expression 37: "y" equals left brace, negative 2 less than "x" less than negative 1 : 0 , negative 1 less than "x" less than 1 : "x" , 1 less than "x" less than 2 : 0 , right bracey=−2<x<−1:0,−1<x<1:x,1<x<2:0
37
Expression 38: Start sum from "n" equals 1 to "M" , end sum, left parenthesis, negative StartFraction, 2 Over "n" pi , EndFraction cos left parenthesis, StartFraction, "n" pi Over 2 , EndFraction , right parenthesis plus StartFraction, 4 Over left parenthesis, "n" pi , right parenthesis squared , EndFraction sin left parenthesis, StartFraction, "n" pi Over 2 , EndFraction , right parenthesis , right parenthesis sine left parenthesis, StartFraction, "n" pi "x" Over 2 , EndFraction , right parenthesisM∑n=1−2nπcosnπ2+4nπ2sinnπ2sinnπx2
