Evaluate lim x→2^+ √x−2.

Question

Accepted Answer

Hello there, today we're gonna solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem, determine the value of the limit as X approaches five from the right of the square root of X minus five. Awesome. So it appears the problem itself has all the important details that we need to use to solve. So we're ultimately trying to figure out the value of the specific limit. So now that we know that we're trying to figure out the value of this limit that's given to us by the problem itself, let's read off our multiple choice answers to see what our final answer might be. So A is zero, B is five, C is negative one and D is the limit does not exist. OK. So first off, we need to identify the limit expression. So as we should note, our limit is as X approaches five from the right because we have this plus sign because we need to recognize that as X approaches five from the right. And that's we know that it's approaching five from the right, because it has this five to the power of this plus sign. So that's what that symbol indicates. And because we have that positive sign in the power for so it's five to the power of this positive sign. We know that X is approaching five from the right. And we also note, we can note and recall that the expression inside of the square root, which is X minus five will be approaching zero from the positive side as we should recall. So it's very important to recall uh from memory that whenever you see this, where it says the limit as X approaches five to the power of this plus sign, the plus sign means that it's approaching five from the right. And we also need to recall once again that the expression for this case in the square root, which is the X minus five will be approaching zero from the positive side. So our next step is we need to recall a note that since the square root function is continuous and is defined for nonne numbers, the square root of X minus five, and let's write this down and we'll write it in red. This is important. So X minus five will be approaching which I'll do an arrow approaching the square root is zero, which means that the square root is zero is equal to zero. So therefore, without a doubt, our limit, which our limit as X approaches five from the right of the square root of X minus five. This expression. So let's write this down. So our limit of X approaches five from the right of X minus five, this limit will be our, our value of this limit will be equal to zero. So therefore, without a doubt, our final answer has to be the letter A which is zero. Hooray, we did it. So thank you so much for watching. Hopefully that helped and I can't wait to see you in the next video. Bye.

Evaluate lim x→2^+ √x−2.

Key Concepts

Limits

One-Sided Limits

Square Root Function

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