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

  • Page ID
    7947
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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. \(f(x) = \cos x\), \(a = \frac{\pi }{2}\)

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