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Taylor and Maclaurin Polynomials worksheets

Build exact degree-bounded polynomials for exp, sin, cos, ln near 1, and reciprocal functions near 1.

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Build each requested polynomial from exact derivative coefficients. Show the center and keep factorial coefficients exact.

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Exact mathematics in a declared range

This generator uses audited finite templates for the named skill. It provides reproducible practice and worked answers without claiming arbitrary symbolic algebra coverage.

Learning objective

What this activity builds

Translate derivative data at a center into exact Taylor coefficients.

Worked example

Find P3 for ln(x) at a=1.

P3(x)=(x-1)-(x-1)^2/2+(x-1)^3/3.

At 1, the kth nonconstant coefficient is (-1)^(k+1)/k.

Teaching notes

Make the practice count

  • Write the center before differentiating.
  • Stop at the requested degree even when later coefficients exist.
  • Keep factorials exact until simplifying each coefficient.

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Math SheetNameScoreTeacherDateTaylor and Maclaurin PolynomialsBuild each requested polynomial from exact derivative coefficients. Show the center and keep factorial coefficients exact.1.Find the Taylor polynomial through order 5 for f(x)=ln(x) centered at a = 1.2.Find the Taylor polynomial through order 5 for f(x)=sin(x) centered at a = 0.Show your reasoning. Keep exact values unless instructed otherwise.math-sheet.comPage 1 of 3
Math SheetNameScoreTeacherDateTaylor and Maclaurin PolynomialsBuild each requested polynomial from exact derivative coefficients. Show the center and keep factorial coefficients exact.3.Find the Taylor polynomial through order 5 for f(x)=1/x centered at a = 1.4.Find the Taylor polynomial through order 5 for f(x)=e^x centered at a = 0.Show your reasoning. Keep exact values unless instructed otherwise.math-sheet.comPage 2 of 3
Math SheetNameScoreTeacherDateTaylor and Maclaurin PolynomialsBuild each requested polynomial from exact derivative coefficients. Show the center and keep factorial coefficients exact.5.Find the Taylor polynomial through order 4 for f(x)=cos(x) centered at a = 0.6.Find the Taylor polynomial through order 4 for f(x)=e^x centered at a = 1.Show your reasoning. Keep exact values unless instructed otherwise.math-sheet.comPage 3 of 3

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