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    Taylor Polynomials and Comparison Tests for Convergence (4 Problems)

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    1. Find the 3rd-degree Taylor polynomial for f(x) = 1/(2+x) at a = 1.

    2. Comparison Test let .

    3. Comparison Limit let .

    4. Comparison Test .

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    1. Find the 3rd-degree Taylor polynomial for at
    Solution. We use an expansion , when |x|<1,

    So, substituting x by -(x-1)/3, we get

    ...

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