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Mathematics LibreTexts

5.E: Convergence of the Taylor Series: A “Tayl” of Three Remainders (Exercises)

 

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Q1

Find the Integral form, Lagrange form, and Cauchy form of the remainder for Taylor series for the following functions expanded about the given values of \(a\).

  1. \(f(x) = e^x\), \(a = 0\)
  2. \(f(x) = \sqrt{x}\), \(a = 1\)
  3. \(f(x) = (1 + x)^α\), \(a = 0\)
  4. \(f(x) = \frac{1}{x}\), \(a = 3\)
  5. \(f(x) = \ln x\), \(a = 2\)
  6. \(f(x) = \cos x\), \(a = \frac{\pi }{2}\) 

Contributor

  • Eugene Boman (Pennsylvania State University) and Robert Rogers (SUNY Fredonia)