Expression 8: "g" Subscript, 1 , Baseline left parenthesis, "x" , right parenthesis equals 1 minus StartAbsoluteValue, sign left parenthesis, "x" , right parenthesis , EndAbsoluteValueg1x=1−signx
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Expression 9: "g" Subscript, 2 , Baseline left parenthesis, "x" , right parenthesis equals ceiling left parenthesis, StartFraction, left parenthesis, sign left parenthesis, negative "x" plus 1 , right parenthesis minus sign left parenthesis, negative "x" , right parenthesis , right parenthesis Over 2 , EndFraction , right parenthesisg2x=ceilsign−x+1−sign−x2
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Expression 10: "L" left parenthesis, "x" , "y" , right parenthesis equals StartFraction, 1 Over "t" Subscript, "d" "e" "l" , Baseline , EndFraction times Start integral from 0 to "T" , end integral, "g" Subscript, 1 , Baseline left parenthesis, StartFraction, left parenthesis, "x" minus "r" Subscript, 1 , Baseline times cos left parenthesis, "w" Subscript, 1 , Baseline times floor left parenthesis, StartNestedFraction, "t" NestedOver "t" Subscript, "d" "e" "l" , Baseline , EndNestedFraction , right parenthesis times "t" Subscript, "d" "e" "l" , Baseline , right parenthesis minus "c" , right parenthesis Over "r" Subscript, 2 , Baseline times cos left parenthesis, "w" Subscript, 2 , Baseline times floor left parenthesis, StartNestedFraction, "t" NestedOver "t" Subscript, "d" "e" "l" , Baseline , EndNestedFraction , right parenthesis "t" Subscript, "d" "e" "l" , Baseline , right parenthesis minus "r" Subscript, 1 , Baseline times cos left parenthesis, "w" Subscript, 1 , Baseline times floor left parenthesis, StartNestedFraction, "t" NestedOver "t" Subscript, "d" "e" "l" , Baseline , EndNestedFraction , right parenthesis times "t" Subscript, "d" "e" "l" , Baseline , right parenthesis minus "c" , EndFraction minus StartFraction, left parenthesis, "y" minus "r" Subscript, 1 , Baseline times sin left parenthesis, "w" Subscript, 1 , Baseline times floor left parenthesis, StartNestedFraction, "t" NestedOver "t" Subscript, "d" "e" "l" , Baseline , EndNestedFraction , right parenthesis times "t" Subscript, "d" "e" "l" , Baseline , right parenthesis , right parenthesis Over "r" Subscript, 2 , Baseline times sin left parenthesis, "w" Subscript, 2 , Baseline times floor left parenthesis, StartNestedFraction, "t" NestedOver "t" Subscript, "d" "e" "l" , Baseline , EndNestedFraction , right parenthesis times "t" Subscript, "d" "e" "l" , Baseline , right parenthesis minus "r" Subscript, 1 , Baseline times sin left parenthesis, "w" Subscript, 1 , Baseline times floor left parenthesis, StartNestedFraction, "t" NestedOver "t" Subscript, "d" "e" "l" , Baseline , EndNestedFraction , right parenthesis times "t" Subscript, "d" "e" "l" , Baseline , right parenthesis , EndFraction , right parenthesis times "g" Subscript, 2 , Baseline left parenthesis, StartFraction, left parenthesis, "y" minus "r" Subscript, 1 , Baseline times sin left parenthesis, "w" Subscript, 1 , Baseline times floor left parenthesis, StartNestedFraction, "t" NestedOver "t" Subscript, "d" "e" "l" , Baseline , EndNestedFraction , right parenthesis times "t" Subscript, "d" "e" "l" , Baseline , right parenthesis , right parenthesis Over "r" Subscript, 2 , Baseline times sin left parenthesis, "w" Subscript, 2 , Baseline times floor left parenthesis, StartNestedFraction, "t" NestedOver "t" Subscript, "d" "e" "l" , Baseline , EndNestedFraction , right parenthesis times "t" Subscript, "d" "e" "l" , Baseline , right parenthesis minus "r" Subscript, 1 , Baseline times sin left parenthesis, "w" Subscript, 1 , Baseline times floor left parenthesis, StartNestedFraction, "t" NestedOver "t" Subscript, "d" "e" "l" , Baseline , EndNestedFraction , right parenthesis times "t" Subscript, "d" "e" "l" , Baseline , right parenthesis , EndFraction , right parenthesis "d" "t"Lx,y=1tdel·∫T0g1x−r1·cosw1·floorttdel·tdel−cr2·cosw2·floorttdeltdel−r1·cosw1·floorttdel·tdel−c−y−r1·sinw1·floorttdel·tdelr2·sinw2·floorttdel·tdel−r1·sinw1·floorttdel·tdel·g2y−r1·sinw1·floorttdel·tdelr2·sinw2·floorttdel·tdel−r1·sinw1·floorttdel·tdeldt
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Expression 11: ceiling left parenthesis, "L" left parenthesis, "x" , "y" , right parenthesis , right parenthesis equals 2ceilLx,y=2