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Section 4-16 : Taylor Series

For problems 1 & 2 use one of the Taylor Series derived in the notes to determine the Taylor Series for the given function.

  1. \(f\left( x \right) = \cos \left( {4x} \right)\) about \(x = 0\) Solution
  2. \(f\left( x \right) = {x^6}{{\bf{e}}^{2{x^{\,3}}}}\) about \(x = 0\) Solution

For problem 3 – 6 find the Taylor Series for each of the following functions.

  1. \(f\left( x \right) = {{\bf{e}}^{ - 6x}}\) about \(x = - 4\) Solution
  2. \(f\left( x \right) = \ln \left( {3 + 4x} \right)\) about \(x = 0\) Solution
  3. \(\displaystyle f\left( x \right) = \frac{7}{{{x^4}}}\) about \(x = - 3\) Solution
  4. \(f\left( x \right) = 7{x^2} - 6x + 1\) about \(x = 2\) Solution