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A function f(x) is differentiable at x = 1 with f'(1) = 3. Evaluate the limit: lim_(h->0) [f(1 + 3h²) - f(1 - 3h²)] / tan²(h).

1. 13
2. 14
3. 18
4. 17

Correct answer: 18

Solution

By first-order Taylor expansion at x=1, the numerator approaches 6*f'(1)*h² = 18h², and the denominator tan²(h) ~ h², so the limit is 18.

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