expression 1 (Hidden) "I" equals 9I=9
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99
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Expression 3: Start sum from "n" equals 1 to "I" , end sum, left parenthesis, left parenthesis, 0.5 minus 0.5cos left parenthesis, pi times 3 Superscript, "n" , Baseline times left parenthesis, ( 2 "x" minus 1 ) minus StartFraction, floor ( "x" times 3 Superscript, "n" , Baseline ) Over 3 Superscript, "n" , Baseline , EndFraction , right parenthesis , right parenthesis , right parenthesis times left parenthesis, 1 minus StartAbsoluteValue, 1 minus mod left parenthesis, floor ( "x" times 3 Superscript, "n" , Baseline ) , 3 , right parenthesis , EndAbsoluteValue , right parenthesis times Start product from "k" equals 1 to "n" minus 1, end product, StartAbsoluteValue, 1 minus mod left parenthesis, floor ( "x" times 3 Superscript, "k" , Baseline ) , 3 , right parenthesis , EndAbsoluteValue , right parenthesis left brace, 0 less than "x" less than 1 , right brace Has graph. To audio trace, press ALT+T.I∑n=10.5−0.5cosπ·3n·(2x−1)−floor(x·3n)3n·1−1−modfloor(x·3n),3·n−1∏k=11−modfloor(x·3k),30<x<1
expression 4 (Hidden) Start sum from "n" equals 1 to "I" , end sum, left parenthesis, left parenthesis, 0.5 minus 0.5cos left parenthesis, pi times 3 Superscript, "n" , Baseline times left parenthesis, "x" minus StartFraction, floor ( ( 0.5 "x" plus 0.5 ) 3 Superscript, "n" , Baseline ) Over 3 Superscript, "n" , Baseline , EndFraction , right parenthesis , right parenthesis , right parenthesis times left parenthesis, 1 minus StartAbsoluteValue, 1 minus mod left parenthesis, floor left parenthesis, ( 0.5 "x" plus 0.5 ) 3 Superscript, "n" , Baseline , right parenthesis , 3 , right parenthesis , EndAbsoluteValue , right parenthesis times Start product from "k" equals 1 to "n" minus 1, end product, StartAbsoluteValue, 1 minus mod left parenthesis, floor left parenthesis, ( 0.5 "x" plus 0.5 ) 3 Superscript, "k" , Baseline , right parenthesis , 3 , right parenthesis , EndAbsoluteValue , right parenthesis left brace, negative 1 less than "x" less than 1 , right braceI∑n=10.5−0.5cosπ·3n·x−floor((0.5x+0.5)3n)3n·1−1−modfloor(0.5x+0.5)3n,3·n−1∏k=11−modfloor(0.5x+0.5)3k,3−1<x<1
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expression 6 (Hidden) Start sum from "n" equals 1 to "I" , end sum, left parenthesis, sin left parenthesis, pi ( 2 "x" minus 1 ) times 3 Superscript, "n" , Baseline , right parenthesis times left parenthesis, 1 minus StartAbsoluteValue, 1 minus mod left parenthesis, floor ( "x" times 3 Superscript, "n" , Baseline ) , 3 , right parenthesis , EndAbsoluteValue , right parenthesis times Start product from "k" equals 1 to "n" minus 1, end product, StartAbsoluteValue, 1 minus mod left parenthesis, floor ( "x" times 3 Superscript, "k" , Baseline ) , 3 , right parenthesis , EndAbsoluteValue , right parenthesis left brace, 0 less than "x" less than 1 , right braceI∑n=1sinπ(2x−1)·3n·1−1−modfloor(x·3n),3·n−1∏k=11−modfloor(x·3k),30<x<1
expression 7 (Hidden) Start sum from "n" equals 1 to "I" , end sum, left parenthesis, sin left parenthesis, pi "x" times 3 Superscript, "n" , Baseline , right parenthesis times left parenthesis, 1 minus StartAbsoluteValue, 1 minus mod left parenthesis, floor left parenthesis, ( 0.5 "x" plus 0.5 ) times 3 Superscript, "n" , Baseline , right parenthesis , 3 , right parenthesis , EndAbsoluteValue , right parenthesis times Start product from "k" equals 1 to "n" minus 1, end product, StartAbsoluteValue, 1 minus mod left parenthesis, floor left parenthesis, ( 0.5 "x" plus 0.5 ) times 3 Superscript, "k" , Baseline , right parenthesis , 3 , right parenthesis , EndAbsoluteValue , right parenthesis left brace, negative 1 less than "x" less than 1 , right braceI∑n=1sinπx·3n·1−1−modfloor(0.5x+0.5)·3n,3·n−1∏k=11−modfloor(0.5x+0.5)·3k,3−1<x<1
Expression 8:
expression 9 (Hidden) left parenthesis, .5 minus .5cos left parenthesis, min left parenthesis, max left parenthesis, "x" , StartFraction, 1 Over 3 to the 1st power , EndFraction , right parenthesis , StartFraction, 2 Over 3 to the 1st power , EndFraction , right parenthesis times 2 pi times 3 to the 1st power , right parenthesis , right parenthesis.5−.5cosminmaxx,131,231·2π·31
Expression 10:
expression 11 (Hidden) left parenthesis, .5 minus .5cos left parenthesis, min left parenthesis, max left parenthesis, "x" , StartFraction, 1 Over 3 squared , EndFraction , right parenthesis , StartFraction, 2 Over 3 squared , EndFraction , right parenthesis times 2 pi times 3 squared , right parenthesis , right parenthesis.5−.5cosminmaxx,132,232·2π·32
expression 12 (Hidden) left parenthesis, .5 minus .5cos left parenthesis, min left parenthesis, max left parenthesis, "x" , StartFraction, 1 plus 2 times 3 to the 1st power Over 3 squared , EndFraction , right parenthesis , StartFraction, 2 plus 2 times 3 to the 1st power Over 3 squared , EndFraction , right parenthesis times 2 pi times 3 squared , right parenthesis , right parenthesis.5−.5cosminmaxx,1+2·3132,2+2·3132·2π·32
Expression 13:
expression 14 (Hidden) left parenthesis, .5 minus .5cos left parenthesis, min left parenthesis, max left parenthesis, "x" , StartFraction, 1 Over 3 cubed , EndFraction , right parenthesis , StartFraction, 2 Over 3 cubed , EndFraction , right parenthesis times 2 pi times 3 cubed , right parenthesis , right parenthesis.5−.5cosminmaxx,133,233·2π·33
expression 15 (Hidden) left parenthesis, .5 minus .5cos left parenthesis, min left parenthesis, max left parenthesis, "x" , StartFraction, 1 plus 2 times 3 to the 1st power Over 3 cubed , EndFraction , right parenthesis , StartFraction, 2 plus 2 times 3 to the 1st power Over 3 cubed , EndFraction , right parenthesis times 2 pi times 3 cubed , right parenthesis , right parenthesis.5−.5cosminmaxx,1+2·3133,2+2·3133·2π·33
expression 16 (Hidden) left parenthesis, .5 minus .5cos left parenthesis, min left parenthesis, max left parenthesis, "x" , StartFraction, 1 plus 2 times 3 squared Over 3 cubed , EndFraction , right parenthesis , StartFraction, 2 plus 2 times 3 squared Over 3 cubed , EndFraction , right parenthesis times 2 pi times 3 cubed , right parenthesis , right parenthesis.5−.5cosminmaxx,1+2·3233,2+2·3233·2π·33
expression 17 (Hidden) left parenthesis, .5 minus .5cos left parenthesis, min left parenthesis, max left parenthesis, "x" , StartFraction, 1 plus 2 times left parenthesis, 3 squared plus 3 to the 1st power , right parenthesis Over 3 cubed , EndFraction , right parenthesis , StartFraction, 2 plus 2 times left parenthesis, 3 squared plus 3 to the 1st power , right parenthesis Over 3 cubed , EndFraction , right parenthesis times 2 pi times 3 cubed , right parenthesis , right parenthesis.5−.5cosminmaxx,1+2·32+3133,2+2·32+3133·2π·33
Expression 18:
expression 19 (Hidden) left parenthesis, .5 minus .5cos left parenthesis, min left parenthesis, max left parenthesis, "x" , StartFraction, 1 Over 3 to the 4th power , EndFraction , right parenthesis , StartFraction, 2 Over 3 to the 4th power , EndFraction , right parenthesis times 2 pi times 3 to the 4th power , right parenthesis , right parenthesis.5−.5cosminmaxx,134,234·2π·34
expression 20 (Hidden) left parenthesis, .5 minus .5cos left parenthesis, min left parenthesis, max left parenthesis, "x" , StartFraction, 1 plus 2 times 3 to the 1st power Over 3 to the 4th power , EndFraction , right parenthesis , StartFraction, 2 plus 2 times 3 to the 1st power Over 3 to the 4th power , EndFraction , right parenthesis times 2 pi times 3 to the 4th power , right parenthesis , right parenthesis.5−.5cosminmaxx,1+2·3134,2+2·3134·2π·34
expression 21 (Hidden) left parenthesis, .5 minus .5cos left parenthesis, min left parenthesis, max left parenthesis, "x" , StartFraction, 1 plus 2 times 3 squared Over 3 to the 4th power , EndFraction , right parenthesis , StartFraction, 2 plus 2 times 3 squared Over 3 to the 4th power , EndFraction , right parenthesis times 2 pi times 3 to the 4th power , right parenthesis , right parenthesis.5−.5cosminmaxx,1+2·3234,2+2·3234·2π·34
expression 22 (Hidden) left parenthesis, .5 minus .5cos left parenthesis, min left parenthesis, max left parenthesis, "x" , StartFraction, 1 plus 2 times left parenthesis, 3 squared plus 3 to the 1st power , right parenthesis Over 3 to the 4th power , EndFraction , right parenthesis , StartFraction, 2 plus 2 times left parenthesis, 3 squared plus 3 to the 1st power , right parenthesis Over 3 to the 4th power , EndFraction , right parenthesis times 2 pi times 3 to the 4th power , right parenthesis , right parenthesis.5−.5cosminmaxx,1+2·32+3134,2+2·32+3134·2π·34
expression 23 (Hidden) left parenthesis, .5 minus .5cos left parenthesis, min left parenthesis, max left parenthesis, "x" , StartFraction, 1 plus 2 times 3 cubed Over 3 to the 4th power , EndFraction , right parenthesis , StartFraction, 2 plus 2 times 3 cubed Over 3 to the 4th power , EndFraction , right parenthesis times 2 pi times 3 to the 4th power , right parenthesis , right parenthesis.5−.5cosminmaxx,1+2·3334,2+2·3334·2π·34
expression 24 (Hidden) left parenthesis, .5 minus .5cos left parenthesis, min left parenthesis, max left parenthesis, "x" , StartFraction, 1 plus 2 times left parenthesis, 3 cubed plus 3 to the 1st power , right parenthesis Over 3 to the 4th power , EndFraction , right parenthesis , StartFraction, 2 plus 2 times left parenthesis, 3 cubed plus 3 to the 1st power , right parenthesis Over 3 to the 4th power , EndFraction , right parenthesis times 2 pi times 3 to the 4th power , right parenthesis , right parenthesis.5−.5cosminmaxx,1+2·33+3134,2+2·33+3134·2π·34
expression 25 (Hidden) left parenthesis, .5 minus .5cos left parenthesis, min left parenthesis, max left parenthesis, "x" , StartFraction, 1 plus 2 times left parenthesis, 3 cubed plus 3 squared , right parenthesis Over 3 to the 4th power , EndFraction , right parenthesis , StartFraction, 2 plus 2 times left parenthesis, 3 cubed plus 3 squared , right parenthesis Over 3 to the 4th power , EndFraction , right parenthesis times 2 pi times 3 to the 4th power , right parenthesis , right parenthesis.5−.5cosminmaxx,1+2·33+3234,2+2·33+3234·2π·34
expression 26 (Hidden) left parenthesis, .5 minus .5cos left parenthesis, min left parenthesis, max left parenthesis, "x" , StartFraction, 1 plus 2 times left parenthesis, 3 cubed plus 3 squared plus 3 to the 1st power , right parenthesis Over 3 to the 4th power , EndFraction , right parenthesis , StartFraction, 2 plus 2 times left parenthesis, 3 cubed plus 3 squared plus 3 to the 1st power , right parenthesis Over 3 to the 4th power , EndFraction , right parenthesis times 2 pi times 3 to the 4th power , right parenthesis , right parenthesis.5−.5cosminmaxx,1+2·33+32+3134,2+2·33+32+3134·2π·34
Expression 27:
expression 28 (Hidden) left parenthesis, .5 minus .5cos left parenthesis, min left parenthesis, max left parenthesis, "x" , StartFraction, 1 Over 3 to the 5th power , EndFraction , right parenthesis , StartFraction, 2 Over 3 to the 5th power , EndFraction , right parenthesis times 2 pi times 3 to the 5th power , right parenthesis , right parenthesis.5−.5cosminmaxx,135,235·2π·35
expression 29 (Hidden) left parenthesis, .5 minus .5cos left parenthesis, min left parenthesis, max left parenthesis, "x" , StartFraction, 7 Over 3 to the 5th power , EndFraction , right parenthesis , StartFraction, 8 Over 3 to the 5th power , EndFraction , right parenthesis times 2 pi times 3 to the 5th power , right parenthesis , right parenthesis.5−.5cosminmaxx,735,835·2π·35
expression 30 (Hidden) left parenthesis, .5 minus .5cos left parenthesis, min left parenthesis, max left parenthesis, "x" , StartFraction, 19 Over 3 to the 5th power , EndFraction , right parenthesis , StartFraction, 20 Over 3 to the 5th power , EndFraction , right parenthesis times 2 pi times 3 to the 5th power , right parenthesis , right parenthesis.5−.5cosminmaxx,1935,2035·2π·35
expression 31 (Hidden) left parenthesis, .5 minus .5cos left parenthesis, min left parenthesis, max left parenthesis, "x" , StartFraction, 25 Over 3 to the 5th power , EndFraction , right parenthesis , StartFraction, 26 Over 3 to the 5th power , EndFraction , right parenthesis times 2 pi times 3 to the 5th power , right parenthesis , right parenthesis.5−.5cosminmaxx,2535,2635·2π·35
expression 32 (Hidden) left parenthesis, .5 minus .5cos left parenthesis, min left parenthesis, max left parenthesis, "x" , StartFraction, 55 Over 3 to the 5th power , EndFraction , right parenthesis , StartFraction, 56 Over 3 to the 5th power , EndFraction , right parenthesis times 2 pi times 3 to the 5th power , right parenthesis , right parenthesis.5−.5cosminmaxx,5535,5635·2π·35
expression 33 (Hidden) left parenthesis, .5 minus .5cos left parenthesis, min left parenthesis, max left parenthesis, "x" , StartFraction, 61 Over 3 to the 5th power , EndFraction , right parenthesis , StartFraction, 62 Over 3 to the 5th power , EndFraction , right parenthesis times 2 pi times 3 to the 5th power , right parenthesis , right parenthesis.5−.5cosminmaxx,6135,6235·2π·35
expression 34 (Hidden) left parenthesis, .5 minus .5cos left parenthesis, min left parenthesis, max left parenthesis, "x" , StartFraction, 73 Over 3 to the 5th power , EndFraction , right parenthesis , StartFraction, 74 Over 3 to the 5th power , EndFraction , right parenthesis times 2 pi times 3 to the 5th power , right parenthesis , right parenthesis.5−.5cosminmaxx,7335,7435·2π·35
expression 35 (Hidden) left parenthesis, .5 minus .5cos left parenthesis, min left parenthesis, max left parenthesis, "x" , StartFraction, 79 Over 3 to the 5th power , EndFraction , right parenthesis , StartFraction, 80 Over 3 to the 5th power , EndFraction , right parenthesis times 2 pi times 3 to the 5th power , right parenthesis , right parenthesis.5−.5cosminmaxx,7935,8035·2π·35
expression 36 (Hidden) left parenthesis, .5 minus .5cos left parenthesis, min left parenthesis, max left parenthesis, "x" , StartFraction, 163 Over 3 to the 5th power , EndFraction , right parenthesis , StartFraction, 164 Over 3 to the 5th power , EndFraction , right parenthesis times 2 pi times 3 to the 5th power , right parenthesis , right parenthesis.5−.5cosminmaxx,16335,16435·2π·35
expression 37 (Hidden) left parenthesis, .5 minus .5cos left parenthesis, min left parenthesis, max left parenthesis, "x" , StartFraction, 169 Over 3 to the 5th power , EndFraction , right parenthesis , StartFraction, 170 Over 3 to the 5th power , EndFraction , right parenthesis times 2 pi times 3 to the 5th power , right parenthesis , right parenthesis.5−.5cosminmaxx,16935,17035·2π·35
expression 38 (Hidden) left parenthesis, .5 minus .5cos left parenthesis, min left parenthesis, max left parenthesis, "x" , StartFraction, 181 Over 3 to the 5th power , EndFraction , right parenthesis , StartFraction, 182 Over 3 to the 5th power , EndFraction , right parenthesis times 2 pi times 3 to the 5th power , right parenthesis , right parenthesis.5−.5cosminmaxx,18135,18235·2π·35
expression 39 (Hidden) left parenthesis, .5 minus .5cos left parenthesis, min left parenthesis, max left parenthesis, "x" , StartFraction, 187 Over 3 to the 5th power , EndFraction , right parenthesis , StartFraction, 188 Over 3 to the 5th power , EndFraction , right parenthesis times 2 pi times 3 to the 5th power , right parenthesis , right parenthesis.5−.5cosminmaxx,18735,18835·2π·35
expression 40 (Hidden) left parenthesis, .5 minus .5cos left parenthesis, min left parenthesis, max left parenthesis, "x" , StartFraction, 217 Over 3 to the 5th power , EndFraction , right parenthesis , StartFraction, 218 Over 3 to the 5th power , EndFraction , right parenthesis times 2 pi times 3 to the 5th power , right parenthesis , right parenthesis.5−.5cosminmaxx,21735,21835·2π·35
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powered by
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"a" squareda2
"a" Superscript, "b" , Baselineab
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greater than>
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times×
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less than or equal to≤
greater than or equal to≥
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