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Answer 1

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Answer 2

Solving a Limit

To solve the limit, we need to evaluate the expression and find the value it approaches as the variable approaches a certain value. The given limit is:

Lim x → 1 (4x^4 - 5x^2 + 1) / (x^2 - 1)

To solve this limit, we can factorize the numerator and denominator and simplify the expression. Let's break it down step by step:

Step 1: Factorize the numerator and denominator: - The numerator can be factored as (2x^2 - 1)(2x^2 - 1). - The denominator can be factored as (x - 1)(x + 1).

Step 2: Simplify the expression: - Now, we can cancel out the common factors in the numerator and denominator. - After canceling out the common factors, we are left with (2x^2 - 1) / (x + 1).

Step 3: Evaluate the limit: - To find the limit as x approaches 1, we substitute x = 1 into the simplified expression. - Plugging in x = 1, we get (2(1)^2 - 1) / (1 + 1) = (2 - 1) / 2 = 1/2.

Therefore, the limit of the given expression as x approaches 1 is 1/2.

Please note that the provided solution is based on the given expression and the steps involved in solving it.