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?

c. limx→0− f(x) = 0

Accepted Answer

Below 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 from the left of F of X is equal to 2. So it appears for this particular problem, we're asked to take this statement, which once again is the limit, as X approaches 1 from the left of F of X is equal to 2, and we're trying to take this statement based on our graph of Y equals F of X, and we're trying to see if this statement is true or false. So it's either going to be a true or B false. So looking at our graph for Y equals F of X really quickly before we start solving, let's, as we can see, we have what appears to be two curves, but it's technically the same curve because as you can see, it starts at -11. And then it goes across until it touches the X axis at 01, and as you can see, it has a hole or a discontinuity. So then it jumps from the hole down to what appears to be the origin point, and then it forms a semic circle shape or an upside down inverted parabola, where it starts at the left, and then it goes to where there's another discontinuity or a hole at 02. So with that said, as you could see, it starts with a straight linear uh linear looking curve. At -11, and then it goes to 01, and then it jumps to 00, and then it curves up to 11, and then it curves down to 02. So, and then there's also a solid point at 12, as we could see, because there's a red, a solid red dot, so there's a coordinate point there. And once again, our curve in red is Y equals F of X. Awesome. So now that we have a good visualization of what's happening for this particular prong, as you can see from the graph, as X approaches 1 from the left, the function will approach a value of 1. So thus we could write that the limit as X approaches 1 from the left. That's what that negative symbol and the power means. So as the limit as X approaches 1 from the left of F of X is equal to 1, and because we just determined that the limit as X approaches 1 from the left of F of X is equal to 1, our current statement, which states that the limit as X approaches 1 from the left of F of X equals 2, has to be false. We also need to note that the function value at X equals 1 is 2, so let's make a note of that. So, X equals 1. Is 2, but in limits. But however, in this particular case, we are interested in the value, if finite, at which the function approaches 1 from the left and not the actual function value. So therefore, our current statement is false, so our final answer has to be the letter B 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?

c. limx→0− f(x) = 0

Key Concepts

Limits

One-Sided Limits

Graphical Interpretation of Limits

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