Use l’Hôpital’s rule to find the limits in Exercises 7–52.
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Question

Use l’Hôpital’s rule to find the limits in Exercises 7–52.

7. lim (x → 2) (x - 2) / (x² - 4)

Accepted Answer

Welcome back, everyone. Evaluate the limit using Lapital's rule. Limit as X approaches 3 of X2 minus 9 divided by X minus 3. A says 3, B says 6, C says 9, and D says infinity. For this problem, let's begin by rewriting the limit. S X approaches 3 of X2 minus 9 divided by, I'm divided by X minus 3. The first step is to check if we get the correct and determinant form. So we're going to substitute X equals 3 into the function, which gives us 32 minus 9 in the numerator and 3 minus 3 in the denominator. When we perform the calculations, we're going to get 0 in the numerator and 0 in the denominator. 0 divided by 0 is a suitable form for the rule. So we're going to apply. Lapitals through from here. Let's remember that according to the rule, we're taking the derivative of the numerator and dividing by the derivative of the denominator. In the numerator, the derivative of X2 is 2 X, the derivative of -9 is 0 because -9 is a constant. So we basically get 2 X in the numerator. And in the denominator, the derivative of X is 1, we're subtracting the derivative of a constant which is 0. So 1 minus 0 gives us 1. Now, we're evaluating 2 X divided by 1, which is simply 2 X. And our goal is to attempt substitution once again. So we get 2 multiplied by 3, which is now a finite value 6, meaning we have arrived at the final limit which corresponds to the answer choice B. Thank you for watching.

Use l’Hôpital’s rule to find the limits in Exercises 7–52.7. lim (x → 2) (x - 2) / (x² - 4)

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Use l’Hôpital’s rule to find the limits in Exercises 7–52.

7. lim (x → 2) (x - 2) / (x² - 4)