Expression 4: "s" left parenthesis, "x" , right parenthesis equals Start sum from "k" equals 0 to "N" , end sum, left parenthesis, negative 1 , right parenthesis Superscript, "k" , Baseline StartFraction, 1 Over left parenthesis, 2 "k" plus 1 , right parenthesis ! , EndFraction "x" Superscript, 2 "k" plus 1 , Baselinesx=N∑k=0−1k12k+1!x2k+1
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Expression 5: 10 "s" left parenthesis, "x" , right parenthesis10sx
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Expression 6: negative StartFraction, log left parenthesis, abs left parenthesis, "s" left parenthesis, "x" , right parenthesis minus sin left parenthesis, "x" , right parenthesis , right parenthesis , right parenthesis Over log left parenthesis, 10 , right parenthesis , EndFraction left brace, 0 less than "x" , right brace−logabssx−sinxlog100<x
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Expression 7: sine left parenthesis, 10 "x" , right parenthesis minus 10sin10x−10
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Expression 8: "s" left parenthesis, 10 "x" , right parenthesis minus 10s10x−10