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Define the following limits: L1 = lim(x->0) (sin(2x) + cos(x) - 1)/x, L2 = lim(x->infinity) (sqrt(x² - x) - x), L3 = lim(x->0+) x^(ln(1/x)), and L4 = lim(x->4) (x² - 3x)/(x² - x). Evaluate L1*L2 + L3 + 1/L4.

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

Correct answer: 2

Solution

Computing each limit: L1=2, L2=-1/2, L3=1, L4=1/3. Then L1*L2 + L3 + 1/L4 = 2*(-1/2) + 1 + 3 = -1 + 1 + 3 = 3.

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