1. (30 points) Use 0-to $3^{rd}$ order Taylor series of $f(x) = \sqrt{x+3}$ about $x = 0.5$ to approximate $f(1)$. Evaluate the true error for each case.
Added by Ronald F.
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5$ to approximate $f(1)$. We also need to evaluate the true error for each approximation. First, let's find the derivatives of $f(x)$ and evaluate them at $x = 0.5$. $f(x) = (x+3)^{1/2}$ $f'(x) = \frac{1}{2}(x+3)^{-1/2}$ $f''(x) = Show more…
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