Calculus: Several Taylor Polynomials for sin(x) on one graph
Expression 4: "T" Subscript, 5 , Baseline left parenthesis, "x" , right parenthesis equals "x" minus StartFraction, "x" cubed Over 3 ! , EndFraction plus StartFraction, "x" to the 5th power Over 5 ! , EndFractionT5x=x−x33!+x55!
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Expression 5: "T" Subscript, 7 , Baseline left parenthesis, "x" , right parenthesis equals "x" minus StartFraction, "x" cubed Over 3 ! , EndFraction plus StartFraction, "x" to the 5th power Over 5 ! , EndFraction minus StartFraction, "x" to the 7th power Over 7 ! , EndFractionT7x=x−x33!+x55!−x77!
5
Expression 6: "T" Subscript, 9 , Baseline left parenthesis, "x" , right parenthesis equals "x" minus StartFraction, "x" cubed Over 3 ! , EndFraction plus StartFraction, "x" to the 5th power Over 5 ! , EndFraction minus StartFraction, "x" to the 7th power Over 7 ! , EndFraction plus StartFraction, "x" to the 9th power Over 9 ! , EndFractionT9x=x−x33!+x55!−x77!+x99!
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Expression 7: "T" Subscript, 11 , Baseline left parenthesis, "x" , right parenthesis equals "x" minus StartFraction, "x" cubed Over 3 ! , EndFraction plus StartFraction, "x" to the 5th power Over 5 ! , EndFraction minus StartFraction, "x" to the 7th power Over 7 ! , EndFraction plus StartFraction, "x" to the 9th power Over 9 ! , EndFraction minus StartFraction, "x" to the 11th power Over 11 ! , EndFractionT11x=x−x33!+x55!−x77!+x99!−x1111!
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Expression 8: "T" Subscript, 13 , Baseline left parenthesis, "x" , right parenthesis equals "x" minus StartFraction, "x" cubed Over 3 ! , EndFraction plus StartFraction, "x" to the 5th power Over 5 ! , EndFraction minus StartFraction, "x" to the 7th power Over 7 ! , EndFraction plus StartFraction, "x" to the 9th power Over 9 ! , EndFraction minus StartFraction, "x" to the 11th power Over 11 ! , EndFraction plus StartFraction, "x" to the 13th power Over 13 ! , EndFractionT13x=x−x33!+x55!−x77!+x99!−x1111!+x1313!