Expression 5: "s" Subscript, "t" "h" , Baseline left parenthesis, "x" , right parenthesis equals left brace, "x" less than or equal to 0 : 0 , "x" greater than or equal to 1 : 1 , StartFraction, 1 minus exp left parenthesis, negative 6 "x" squared , right parenthesis Over 1 plus exp left parenthesis, negative 6 "x" squared , right parenthesis , EndFraction , right bracesthx=x≤0:0,x≥1:1,1−exp−6x21+exp−6x2
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Expression 6: "s" left parenthesis, "x" , "a" , "b" , right parenthesis equals "s" Subscript, "H" , Baseline left parenthesis, StartFraction, "x" minus "a" Over "b" minus "a" , EndFraction , right parenthesissx,a,b=sHx−ab−a
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Expression 7: "f" left parenthesis, "x" , right parenthesis equals left brace, "x" less than .1 : "s" left parenthesis, "x" , .1 , negative .1 , right parenthesis , "x" less than .9 : "s" left parenthesis, "x" , .1 , .9 , right parenthesis , "s" left parenthesis, "x" , 1.1 , .9 , right parenthesis , right bracefx=x<.1:sx,.1,−.1,x<.9:sx,.1,.9,sx,1.1,.9
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Expression 8: "f" left parenthesis, mod left parenthesis, "x" , 1 , right parenthesis , right parenthesis Has graph. To audio trace, press ALT+T.fmodx,1
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Expression 9: "x" minus 1 half minus .5 3 3 left parenthesis, "f" left parenthesis, mod left parenthesis, "x" , 1 , right parenthesis , right parenthesis minus 1 half , right parenthesis Has graph. To audio trace, press ALT+T.x−12−.533fmodx,1−12
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Expression 10: StartFraction, "d" Over "d" "x" , EndFraction "f" left parenthesis, mod left parenthesis, "x" , 1 , right parenthesis , right parenthesisddxfmodx,1