In a temperature measuring system, a signal x, representing the temperature to be measured, is produced by a transducer such that 2≤x≤3. The signal is then amplified by an amplifier whose output y is defined by the function f(x) as: y = f(x) = ln(1 + x) (a) Assuming an accuracy of at least three decimal places is required, determine the quadratic Taylor's polynomial that approximates the function f(x) around the point x=2.5. (b) Use the above approximating polynomial to calculate estimates of y(2.5) and y(2.8). (c) Hence, calculate the errors in the estimates in (b) above and comment on your answers.

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