Analyze lim x→∞ f(x) and lim x→−∞ f(x), and then identify any horizontal asymptotes.
f(x) = (x⁴ − 1)/(x^2−1)

Guida verificata passo dopo passo

Step 1: Identify the degrees of the numerator and the denominator.

Step 2: Compare the degrees of the numerator and the denominator.

Step 3: Analyze lim x→∞ f(x) by dividing each term by the highest power of x in the denominator.

Step 4: Analyze lim x→−∞ f(x) using the same method as in Step 3.

Step 5: Determine the horizontal asymptotes based on the limits found in Steps 3 and 4.

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Limits at Infinity

Limits at infinity examine the behavior of a function as the input approaches positive or negative infinity. This analysis helps determine the end behavior of the function, which is crucial for identifying horizontal asymptotes. For rational functions, the degrees of the numerator and denominator play a significant role in determining the limit.

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