Expression 3: "f" left parenthesis, "x" , right parenthesis equals negative StartFraction, 1 Over ln left parenthesis, 10 , right parenthesis , EndFraction left parenthesis, "x" positive StartFraction, "x" squared Over 4 , EndFraction plus StartFraction, "x" cubed Over 9 , EndFraction plus StartFraction, "x" to the 4th power Over 16 , EndFraction plus StartFraction, "x" to the 5th power Over 25 , EndFraction plus StartFraction, "x" to the 6th power Over 36 , EndFraction plus StartFraction, "x" to the 7th power Over 49 , EndFraction plus StartFraction, "x" to the 8th power Over 64 , EndFraction plus StartFraction, "x" to the 9th power Over 81 , EndFraction , right parenthesisfx=−1ln10x+x24+x39+x416+x525+x636+x749+x864+x981
3
Notice how the MacLaurin series starts to diverge from the function once you've gone beyond x = + or -1.
4
Expression 5: "x" equals 1x=1
negative 10−10
1010
5
Expression 6: "x" equals negative 1x=−1
negative 10−10
1010
6
7
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Notice how you have a hole here at x = 0 on the original function