Finding Limits Graphically

L...

Question

Finding Limits Graphically

Let f(x) = {3 - x , x < 2

2, x = 2

x/2, x > 2

c. Find limx→−1− f(x) and limx→−1+ f(x).

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. Consider the graph of F of X is equal to curly bracket of. 4 minus X X is less than 31, X is equal to 3, and X minus 2X is greater than 3. Determine the limit as X approaches 0 from the right of F of X and the limit as X approaches 0 from the left of F of X. Awesome. So it appears for this particular problem, we're asked to solve for two separate answers. So we're asked to consider our graph of F of X, which is given to us by the problem itself, so we're told. What the graph of F of X is equal to and we're also given a graph of F of X, and we're asked to determine the limit as X approaches 0 from the right of F of X. That's our first answer. And we're also asked to determine the limit as X approaches 0 from the left of F of X as well, and that is our second and final answer we're ultimately trying to solve for. So with that said, let us focus our attention on finding the limit as X approaches 0 from the right of F of X first. So let's solve for this limit first. Let's let's focus our attention. On as X approaches 0 from the right. So as X approaches 0 from the right, let us note that F of X will approach 4, and once again we can get 4 from looking at our graph, which let's take a moment here to pause and investigate our graph. So our Y axis denotes F of X and our X-axis denotes X, of course, and we have a red curve denoting our curve for F of X, and as you can see, it's in red, and we have a hole at 3.1, and we have a solid point at 3.1, and our curve appears to be a checkmark shape, which it goes. So crosses are FX F of X axis. At 04 and then it also. So, so then it doesn't touch your XXx also it intersects or FX axis, or what would be the Y axis once again at 0.4, and then it straight down like a diagonal line where it reaches our hole and then it bounces back up again in a check a checkmark shape. So with that in mind, so when we look at our graph, once again, we note that when X approaches 0 from the right, F of X will approach 4. So therefore, we can go ahead and write that the limit as X approaches 0 from the right of F of X is going to be equal to 4. Fantastic. So with that said, we can find our second limit now. So this is the limit as X approaches 0 from the left. Of F of X, fantastic. So now, focusing our attention on as X approaches 0 from the left, that will mean that F of X will approach 4 as well. So therefore we can go ahead and write that the limit as X approaches 0 from the left. So the limit as X approaches 0 from the left of F of X will be equal to 4. Fantastic. So, with that said, Our final answers, when we recap, have to be the following. So, once again, our final answers, without a doubt, have to be the limit as X approaches 0 from the right of F of X is equal to 4, and the limit as X approaches 0 from the left of F of X is equal to 4. And that's it. We've officially solved for this problem. 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

Let f(x) = {3 - x , x < 2
2, x = 2
x/2, x > 2

<IMAGE>

c. Find limx→−1− f(x) and limx→−1+ f(x).

Key Concepts

Limits

Piecewise Functions

Graphical Interpretation of Limits

Watch next