Expression 3: "p" Subscript, "t" "o" "n" "b" , Baseline left parenthesis, "n" Subscript, "u" "m" , Baseline , right parenthesis equals left parenthesis, Start sum from "v" Subscript, 4 , Baseline equals 2 to "n" Subscript, "u" "m" , Baseline , end sum, left parenthesis, "i" Subscript, "s" "p" , Baseline left parenthesis, "v" Subscript, 4 , Baseline , right parenthesis , right parenthesis , right parenthesisptonbnum=num∑v4=2ispv4
3
Expression 4: "p" Subscript, "t" "o" "n" "a" , Baseline left parenthesis, "n" Subscript, "u" "m" , Baseline , right parenthesis equals "p" Subscript, "t" "o" "n" "b" , Baseline left parenthesis, "n" Subscript, "u" "m" , Baseline , right parenthesis plus left brace, "i" Subscript, "s" "p" , Baseline left parenthesis, "n" Subscript, "u" "m" , Baseline , right parenthesis equals 1 : 0 , 1 , right braceptonanum=ptonbnum+ispnum=1:0,1
4
Expression 5: "s" Subscript, "b" "e" "t" , Baseline left parenthesis, "a" , "b" , "x" , right parenthesis equals sine left parenthesis, left brace, "b" minus "a" equals 0 : 0 , StartFraction, pi left parenthesis, "x" minus "a" , right parenthesis Over left brace, "b" minus "a" equals 0 , "b" minus "a" , right brace , EndFraction , right brace , right parenthesis left parenthesis, "b" minus "a" , right parenthesissbeta,b,x=sinb−a=0:0,πx−ab−a=0,b−ab−a
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Expression 6: "p" Subscript, "s" "i" "n" "e" , Baseline left parenthesis, "x" , right parenthesis equals "s" Subscript, "b" "e" "t" , Baseline left parenthesis, "n" Subscript, "p" , Baseline left parenthesis, "p" Subscript, "t" "o" "n" "b" , Baseline left parenthesis, floor left parenthesis, "x" , right parenthesis , right parenthesis , right parenthesis , "n" Subscript, "p" , Baseline left parenthesis, "p" Subscript, "t" "o" "n" "a" , Baseline left parenthesis, ceil left parenthesis, "x" , right parenthesis , right parenthesis , right parenthesis , "x" , right parenthesis left parenthesis, 2mod left parenthesis, "p" Subscript, "t" "o" "n" "b" , Baseline left parenthesis, floor left parenthesis, "x" , right parenthesis , right parenthesis , 2 , right parenthesis minus 1 , right parenthesis Has graph. To audio trace, press ALT+T.psinex=sbetnpptonbfloorx,npptonaceilx,x2modptonbfloorx,2−1
