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A differentiable function f satisfies f(0) = 2, f'(0) = 3 and f''(x) = f(x). If A is the area enclosed by y = f(x) in the second quadrant, find [A], where [.] is the greatest integer function.

1. 0
2. 1
3. 2
4. 3

Correct answer: 0

Solution

f(x) = 2.5 e^x - 0.5 e^-x; it is zero at x = (1/2) ln(0.2) ~ -0.805. The second-quadrant area is about 0.76, so [A] = 0.

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