In Exercises 1–6, use l’Hôpital’s Rule to evaluate the limit. ...

Question

In Exercises 1–6, use l’Hôpital’s Rule to evaluate the limit. Then evaluate the limit using a method studied in Chapter 2.

1. lim (x → -2) (x + 2) / (x² - 4)

Accepted Answer

Welcome back, everyone. Use Lapito's rule to evaluate the limit. Limit as X approaches 1 of X2 minus 1 divided by X minus 1. A says 2, B says 1, C says 0, and D says infinity. Let's begin by rewriting the limit. Limit as x approaches 1 of X2 minus 1 divided by X minus 1. First, we have to check if we get an indeterminant form that we need. If we substitute X equals 1, we get 1 squad minus 1 in the numerator. And in the denominator we have 1 minus 1. Calculating, we get 0 in the numerator and 0 in the denominator. 0 divided by 0 is the indeterminate form that works with Lapito's rules, so we can apply the rule. The rule says that we want to differentiate the numerator and the denominator separately, so taking the derivative of X squad minus 1, we get 2 X minus 0, which is simply 2 X. In the denominator, we want to take the derivative of X minus 1, which is 1 minus 0, and that's basically 1. So we get the new function, 2 x divided by 1, which is simply 2 X. And what we have to do from here is again attempt substitution of X equals 1 into our function. So we're going to get 2 multiplied by 1, and this is now a finite value. Meaning the limit is 2, and this corresponds to the answer choice A. Thank you for watching.

In Exercises 1–6, use l’Hôpital’s Rule to evaluate the limit. Then evaluate the limit using a method studied in Chapter 2.1. lim (x → -2) (x + 2) / (x² - 4)

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In Exercises 1–6, use l’Hôpital’s Rule to evaluate the limit. Then evaluate the limit using a method studied in Chapter 2.
1. lim (x → -2) (x + 2) / (x² - 4)