c. Let f(x) = frac{e^{x}-e^{-x}}{x}. The actual values values is f(0.1) = 2.003335000. Find the relative error for the values obtained in parts (b) and (c)

c. Let $f\left(x\right)=\frac{{e}^{x}-{e}^{-x}}{x}$.
The actual values values is $f\left(0.1\right)=2.003335000$. Find the relative error for the values obtained in parts (b) and (c)
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Nichole Watt
The given function is $f\left(x\right)=\frac{{e}^{x}-{e}^{-x}}{x}$.
From the sub part b and c note that, the value of f at 0.1 is 2.05 amd 2
Obtain the relative error at these values as shown below
$\text{Error}\left(b\right)=\frac{|2.003335000-2.05|}{|2.003335000|}$
$\text{Error}\left(b\right)=0.0232937$
$\text{Error}\left(c\right)=\frac{|2.003335000-2|}{|2.003335000|}$
$\text{Error}\left(c\right)=0.00166$
Therefore, the required absolute error are 0.0232937 and 0.00166, respectively