Use l’Hôpital’s Rule to find the limits in Exercises 85–108.

Question

85. lim(x→1) (x² + 3x - 4)/(x - 1)

Accepted Answer

Welcome back, everyone. Compute the limit using Lapital's rule. Limit as X approaches 4 of X2 minus 2X minus 8 divided by X minus 4. A 0 B2, C4, and D6. For this problem, let's rewrite the limit. Limit as x approaches 4. Of X2 minus 2X minus 8. Divided by X minus 4. Remember that the first step is to substitute X equals 4 for every X, which gives us 42 minus 2 multiplied by 4 minus 8. Divided by 4 minus 4, which results In an indeterminate form 0 divided by 0. And for this indeterminant form, we can immediately apply Lapito's rule, which says that we want to differentiate the numerator. And the denominator. Let's find each derivative. For the numerator, we are going to apply the power rule to get 2 X minus 2 multiplied by 1 minus 0, right? The derivative of 8. I'm sorry, -8 is 0 because negative 8 is a constant, and in the denominator. The derivative of X is 1, the derivative of -4 is 0. So we, we basically want to take the limit of 2 X minus 21 X approaches 4. Let's now substitute X equals 4 to get 2 multiplied by 4 minus 2, which is a finite value. It is 6. So the final answer for this problem is option D 6. Thank you for watching.

Use l’Hôpital’s Rule to find the limits in Exercises 85–108.85. lim(x→1) (x² + 3x - 4)/(x - 1)

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Use l’Hôpital’s Rule to find the limits in Exercises 85–108.
85. lim(x→1) (x² + 3x - 4)/(x - 1)