Finding Limits Graphically

Which of the follo...

Question

Finding Limits Graphically

Which of the following statements about the function y = f(x) graphed here are true, and which are false?

e. limx→0 f(x) exists

Accepted Answer

Hello there. Today we're going to 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 validity of the following statement based on the given graph of Y equals F of X. The limit as X approaches 1 of F of X exists. So it appears for this particular prom, we're asked to take our given statement, which once again is the limit as X approaches one of F of X exists, and we're asked to prove that this statement is true or false, based on our provided graph of Y. equals F of X. So now that we know what we're solving for, noting that we're either trying to determine whether our statement is a true or B false, let's take a moment to quickly investigate our graph that is provided to us by the prom itself. So as you can see, we have what appears to be two separate curves, but they're technically the same curve for Y equals FF X. And the reason why it looks like it's two separate curves is because we have a discontinuity. So we have our first part, which looks like our first curve, but it's all part of the same curve, which starts at -11, which is a solid point, and then it leads to 0.1, which which ends in a hole or a discontinuity. So then the curve jumps to 0.0, and then it curves upward to 0, so it goes to 11, so from 00 and then it jumps up to 11, and then it dips back down to 02, where there's another discontinuity, and then there's also a solid point at 12 or 1.2, as we could see in our graph. So, now that we have a good visualization of what's happening in this particular problem, noting once again that our curve is represented in red, let's note that from the graph as X approaches one from the left, the function approaches a value of 1. Moreover, as X approaches 1 from the right, we could see that the function approaches a value of 1 as well. So sense, we can go ahead and write that sense, the limit as X approaches one from the left. That's what that negative symbol in the power means. So as X approaches one from the left of F of X, so once again the limit as X approaches one from the left of F of X is going to be equal to the limit as X approaches 1 from the right. That's what that positive symbol and the power means, of F of X. is going to be equal to 1. So once again, the limit as X approaches 1 from the left of F of X is equal to the limit as X approaches 1 from the right of F of X, which is equal to 1. So this means that it will follow that the limit as X approaches 1 of F of X is going to be equal to 1. And therefore, since the limit exists and is equal to one, our given statement must be true. So that means without a doubt, our final answer has to be a true. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

Finding Limits Graphically

Which of the following statements about the function y = f(x) graphed here are true, and which are false?

e. limx→0 f(x) exists

Key Concepts

Limits

Graphical Interpretation of Limits

Existence of Limits

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