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Compute lim x→3 (x⁴ - 81) / (2x² - 5x - 3)

1. 1
2. 53/12
3. 108/7
4. Limit does not exist

Correct answer: 108/7

Solution

x^4-81 = (x-3)(x+3)(x^2+9) and 2x^2-5x-3 = (2x+1)(x-3). Cancelling (x-3) gives (x+3)(x^2+9)/(2x+1); at x=3 this is 6*18/7 = 108/7.

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