# 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)

Question
Polynomial arithmetic
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)

2020-12-17
The given function is $$f(x) = \frac{e^{x}-e^{-x}}{x}$$.
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
$$\text{Error}(b) = \frac{|2.003335000-2.05|}{|2.003335000|}$$
$$\text{Error}(b) = 0.0232937$$
$$\text{Error}(c) = \frac{|2.003335000-2|}{|2.003335000|}$$
$$\text{Error}(c) = 0.00166$$
Therefore, the required absolute error are 0.0232937 and 0.00166, respectively

### Relevant Questions

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Previous studies show that $$\sigma_1 = 19$$.
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