Determine the following limits.

c. lim x→4 x ...

Question

Determine the following limits.

c. lim x→4 x − 5 / (x − 4)^2

Accepted Answer

Welcome back, everyone. Evaluate the limit. Limit as x approaches -1 of X + 2 divided by X + 1 squared. We're given 4 answer choices A says 0, B-1, C infinity, and D negative infinity. So let's write down the limit. We're given a limit as x approaches -1. And we are evaluating x + 2 divided by x + 12. We begin solving this problem by direct substitution, so we're going to take -1 + 2 in the numerator and in the denominator we're going to get -1 + 1 squad. Now if we simplify, this is going to be equal to -1 + 2, which is 1. And now, at the bottom, we have -1 + 1 which is 00 squared is 0. And we're always going to get a positive number, right? Let's recall the limit existence theorem. The limit as x approaches -1 only exists if the limit as X approaches -1 from the left and the limit as x approaches -1 from the right. Basically, if those are equal to each other. In this case they will be equal to each other because whether we get 0 from the left or 0 from the right, we are squaring it, so we always get a positive number. So the limit itself exists and because we have a ratio between 1 and 0, a number and 0, this gives us a limit of infinity, and this is going to be positive infinity because the two numbers are positive. So our final answer to this problem corresponds to the answer choice C. Thank you for watching.

Determine the following limits.

c. lim x→4 x − 5 / (x − 4)^2

Key Concepts

Limits

Indeterminate Forms

L'Hôpital's Rule

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