Explain why lim x→3^+ √ x−3 / 2−x does not exist.

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 provide a justification on why the limit as X approaches five from the left of the square root of X minus five divided by seven minus X does not exist. Awesome. So it appears for this particular prompt, we're asked to figure out why this specific limit does not exist or trying to figure out a justification for why this specific limit does not exist. So considering that let's read off multiple choice answers to see what our final answer might be for our justification on why this limit does not exist. Awesome. So A is the function of F of X is equal to the square root of X minus five divided by seven minus X is not defined for X is less than seven B is the function of F FX is equal to the square root of X minus five divided by seven minus X is not defined for X equals seven C is the number of the right of five are not in the domain of F of X equals the square root of X minus five divided by seven minus X. And finally D is the numbers to the left of five are not in the domain of F of X equals the square root of X minus five divided by seven minus X. OK. So first off, in order to solve this problem, we need to recall a note that in order for F of X to be equal to the square root of X minus five divided by seven minus X. So in order for this to be defined the ratican of, and let's make, let's write this in red. So I'll put in parentheses. So the Ratican which is X minus five divided by seven minus X. So this is the Ratican has to be Nonne. So denote this as Nn Nonne. So that means, and I'll write this in blue. So that means without a doubt that X minus five divided by seven minus X has to be greater than, or equal to zero. Awesome. So by using algebra, so we're calling and using algebra the solution two and let's write this in black. So the solution two X minus five divided by seven minus X is greater than an equal to zero. The correct answer is the closed interval which whenever we're dealing with a closed interval, we have to put a bracket. So this is equal to the closed bracket of five comma seven parenthesis where the parenthesis means an open interval. So in case you can't remember or don't recall closed bracket. So this bracket, the square bracket means a closed interval. So it's closed at five and open at seven means the parenthesis means an open interval. Awesome. So therefore, without a doubt, we can go ahead and write that F of X is equal to the square root of X minus five divided by seven minus X. So we can say the domain is bracket five comma seven parenthesis. So that is the domain of F FX. So since the numbers to the left of five are not in the domain of the function which is F of X equals the square root of X minus five divided by seven minus X. This specific limit will not exist. So it does. So it's not in the domain. So, so let's put a note. So not in domain. So I did it N ID, so not in domain. And because it's not within the domain of five, because since the numbers left to five are not in the domain, this limit does not exist. So that means without a doubt, our final answer has to be multiple choice answer letter D which once again is the numbers to the left of five are not in the domain of F of X equals the square root of X minus five divided by seven minus X. Thank you so much for watching. Hopefully that helped and I can't wait to see you in the next video. Bye.

Explain why lim x→3^+ √ x−3 / 2−x does not exist.

Key Concepts

Limits

One-Sided Limits

Undefined Expressions

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