Finding One-Sided Limits Algebraically
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Question

Finding One-Sided Limits Algebraically

Find the limits in Exercises 11–20.

a. limx→1+ (√2x (x − 1)) / |x − 1|

Accepted Answer

Welcome back, everyone. In this problem, we want to determine the one-sided limit as X approaches 3 from the left for the function F of X equals X2 multiplied by X minus 3 divided by the absolute value of X minus 3. A says it's 9, B 0, C9, and D says it's 1. Now how can we determine our one-sided limit as X approaches 3 from the left? Well, notice that in F of X we have an absolute value function in the denominator, and the absolute value function behaves differently depending on what direction we are approaching X from. No, in our problem, since we are approaching 3 from the left, OK, then that means X must be less than 3. Therefore, That tells us then that we can use the negative value of X minus 3 for the absolute value of X minus 3 because X is approaching 3 from the left. So we're going to substitute negative X minus 3 into the limit expression. So that tells us then. That the limit as x approaches 3 from the left of F of X is going to be equal to the limit as x approaches 3 from the left of X squared multiplied by X minus 3 divided by the negative value of X minus 3. Here we can cancel X minus 3 from the numerator and denominator and if we divide X squared by -1, that means. It's going to be equal to negative X2. Now if we evaluate the limit, OK, then that means we can directly substitute 3 into our expression, so this is going to be the. The value of -3 squad, which is gonna be -9. Notice that we're looking for the negative value of 3 squared, not negative 3 squared, you know, sometimes students sometimes make that uh error, but it's very important to pay attention to our science. Thus, this tells us then that the one-sided limit of F of X as X approaches 3 from the left is -9. If we look back at our answer choices, that means C is the correct answer. Thanks a lot for watching everyone. I hope this video helped.

Finding One-Sided Limits Algebraically

Find the limits in Exercises 11–20.

a. limx→1+ (√2x (x − 1)) / |x − 1|

Key Concepts

One-Sided Limits

Absolute Value Function

Limit Evaluation Techniques

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