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For the function e^(-x), the linear approximation around x = 2 is

1. (3 - x)e⁻²
2. 1 - x
3. [3 + 2√2 - (1 + √2)x]e⁻²
4. e⁻²

Correct answer: (3 - x)e⁻²

Solution

The linear approximation of a function at a point is given by the formula f(a) + f'(a)(x - a). For the function e^(-x), evaluating at x = 2 gives the correct linear approximation as (3 - x)e⁻², which represents the tangent line at that point.

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