Answer :
The question appears to be about linear approximations and calculating the numerical error for a function at a given point. But without the function and the value of 'a', a direct answer to this question is unattainable. An example was given for better understanding.
The question seems to request an investigation into the linear approximation of an unavailable function f(x) at a given point a, manifesting in L(x) = f(a) + f'(a)(x -a). To evaluate this, a function f(x) and a specific point 'a' should be known.
Because neither is given in the question, a straight answer is unachievable. The same goes for computing the numerical error, which involves comparing the linear approximation to the actual function's value.
However, just to get a feeling for how it works, let's consider y = 2x^2 as an example for f(x). Choosing 'a' as 1, f(a) = 2*(1)^2 = 2, and f'(a)(x-a) yields 4(x - 1). Hence, the linear approximation of f(x) at a is L(x) = 2 + 4(x - 1).
It's imperative to remember that this kind of question needs a function and a value for 'a' to assist in giving an accurate answer.
Learn more about Linear Approximation here:
https://brainly.com/question/1621850
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