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?

b. limx→2 f(x) does not exist

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 -2 of F of X does not exist. Awesome. So it appears for this particular prompt we're asked to take our given graph of Y equals F of X, and we're asked to determine whether or not our statement, which once again is the limit as X approaches -2 of F of X, does not exist, and we're trying to determine whether or not this statement is either a true or B false. So with that said, let us quickly look at our graph to help us better visualize what's happening in this particular prong. And as you can see, we have what appears to be two separate curves, but technically they're the same curve, but there's a discontinuity, so that means that the curve disappears into the hole and then it reappears at another point in the graph and then continues. So, as you could see for our one curve, it's shaped like a fin on a fish or on a dolphin, and it's or maybe like a wave, and it starts at negative, so it goes from 0.1, where there's a hole, and then it goes up where it touches the Y axis at what appears to be 0.2, and then it curves back down to touch our X axis at. 2.0. And then we have a linear part of our curve, which starts at -3-1, and that and that starts with a solid point. Then it goes to where there's a hole or a discontinuity at -2-1, and then it continues to a solid point at -1.1. And we also have another solid point all by itself at -2.2. So now that we have a nice visualization of what's happening in this particular prompt. First off, let us note that from the graph, when we look at it, we can note that as X approaches -2 from the left, the function will approach a value of -1. So therefore, as a result, we can go ahead and write that the limit as X approaches -2 from the left of F of X is going to be equal to -1. And we should be able to note also when we look at our graph that as X approaches -2 from the right, the function will approach a value of -1 as well. So thus we can go ahead and write that the limit as X approaches -2 from the right of F of X is also equal to -1. So, therefore, since the limit as X approaches -2 from the left of F of X is equal to the limit as X approaches -2 from the right of F of X is all equal to -1. So since this is the case, we can go ahead and state that the limit as X approaches -2. Of once again F of X will be equal to -1. So therefore, without a doubt, the limit does indeed exist and will be equal to -1 as we just proved. So therefore, going back to look at our given statement, our given statement It has to be false because the limit as X approaches -2 of F of X does indeed exist. So that means our final answer, without a doubt has to be be false. 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?

b. limx→2 f(x) does not exist

Key Concepts

Limits

Graphical Interpretation of Limits

Existence of Limits

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