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?

f. limx→0 f(x) = 0

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 graph of Y equals F of X. The limit as X approaches 1 of F of X is equal to 1. Awesome. So it appears for this particular problem, we're asked to take our following statement, which once again is the limit as X approaches 1 of F of X is equal to 1, and we're asked to use our graph of Y equals F of X to to prove whether or not our given statement is either a true or B false. So we're trying to prove, once again, we're trying to prove whether or not this statement. Based on our graph is true or false. So now that we know what we're ultimately trying to solve for, let's investigate our graph. Let's look at our graph to see what's happening, to help us better visualize what's going on. So as you can see, we have what appears to be two separate curves, but technically they're the same curve because we have a discontinuity or a hole. So that means that our linear graph, which starts at -11, And it goes to touch our Y axis at 01, so it starts with a solid point and then ends in a hole or a discontinuity. So the linear curve stops at 01 and then it jumps to 0.0, which is the origin point, and then it starts to curve upward to 11, where there appears to be another hole, and then it curves down again to touch our X-axis at 02 where there's a hole. And there's also a solid point, which are solid points are represented by red dots, like filled in red dots. So there's a solid coordinate dot at 1.2. So as you can see, it goes from a linear graph, which is straight, and then it goes into what looks like an inverted parabola or a semicircle or half a circle shape for the second half of our the same curve. And that's it. So, as we could see, we have a good visualization of what's happening. So looking at our graph from the graph, we can see that as X approaches 1 from the left, the function approaches a value of 1. Moreover, if X approaches 1 from the right, the function will also approach a value of 1 as well. So, therefore, we can go ahead and write that sense the limit. As X approaches 1 from the left, which that's what that negative sign in the power means. So 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. That's what that positive symbol in the power means. So once again, the limit as X approaches one from the left of F of X is equal to the limit of the limit as X approaches one from the right of F of X is going to be all equal to 1. So that will mean that it will follow up that the limit, so we could go ahead and write that the limit as X approaches 1 of F of X is also going to be equal to 1. So therefore, our given statement without a doubt has to be true, because once again our statement was the limit as x approaches 1 of F of X equals 1, and we just proved that together. 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?

f. limx→0 f(x) = 0

Key Concepts

Limits

Graphical Interpretation of Limits

Continuity

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