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.

9. lim (t → -3) (t³ - 4t + 15) / (t² - t - 12)

Accepted Answer

Welcome back everyone. Evaluate the limit using Lapital's rule. Limit as X approaches 1 of X cubed minus 1 divided by X2 minus 1. A says 3 halves, B says 1, C says 2/3, and D says 0. For this problem, let's begin by rewriting the limit as X approaches 1 of X cubed minus 1 divided by X2 minus 1. The first step is to check if we get an indeterminate form that we want. So we're going to substitute X equals 1 into the function to get 1 cubed minus 1 divided by 1 squad minus 1. Now, performing calculations, we get 1 minus 1 in the numerator, which is 0 and 1 minus 1 in the denominator, which is also 0. 0 divided by 0 is a suitable form for the rules, so we can go ahead and apply it. The rule says that we want to take the derivative of the numerator and the derivative of the denominator. The derivative of the numerator is the derivative of X cubed minus 1, which is 3 X2 minus 0. That's 3 X2, and the derivative of the denominator is the derivative of X2 minus 1, which is 2 X minus 0. Our next step is to again try and substitute X equals 1 into the functions, so we get 3 multiplied by 1 squared, divided by 2 multiplied by 1. So we get 3 divided by 2, which is 3 halves. Now, it is a finite value, meaning this is the finite, this is the final limit. And the answer corresponds to the answer choice A. Thank you for watching.

Use l’Hôpital’s rule to find the limits in Exercises 7–52.9. lim (t → -3) (t³ - 4t + 15) / (t² - t - 12)

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

9. lim (t → -3) (t³ - 4t + 15) / (t² - t - 12)