Final answer:
The limit as x approaches infinity for the expression (x²-3x-⁴)/(x²-1) is 1.
Step-by-step explanation:
The limit as x approaches infinity for the expression (x²-3x-⁴)/(x²-1) can be found by dividing the leading terms of the numerator and denominator. Since the leading term in both the numerator and denominator is x², we can simplify the expression to (1-3/x⁻¹-⁴/x²)/(1-1/x²).
The limit as x approaches infinity for the expression (x²-3x-⁴)/(x²-1) is 1.
Expanding this expression and canceling out like terms, we get (1-3/x)/(1-1/x²). As x approaches infinity, the terms with x in the denominator become insignificant, and we are left with 1/1, which equals 1
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