Skip to main content\(\newcommand{\deriv}[2]{\displaystyle \frac{d#1}{d#2}}
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The red curve is the graph of
\(f(x) = e^x\) and the blue curve is the graph of the Taylor polynomial
\(p_2(x)\text{.}\) The exact value of
\(e^{0.5}\) is represented by the red point and the approximation given by
\(p_2(0.5)\) is represented by the blue point. The vertical distance between the two points represents the error in the approximation. Note that the error is less than the upper bound we calculated, i.e.,
\(0.03435\text{.}\)