Let’s do some explorations with approximating ex. Ultimately, we want to approximate e^(23. (a) Compute the second degree of the Taylor polynomial of…

  1. Let’s do some explorations with approximating ex. Ultimately, we want to approximate e^(23.5 ).
  2. (a) Compute the second degree of the Taylor polynomial of ex centered at x = 0. Let’s call it T(x).
  3. (b) When is err(x) = |e^x − T (x)| < 0.1?
  4. (c) Give the value for ln(10)? Let’s call that a. What is ea?
  5. (d) Compute 23.5. Let M be the integer part of that fraction. Compute out d = a 23.5 − M ∗ a, both roughly and accurately.

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