![]() Well let's see, as x approaches oneįrom the left-hand side, it looks like we areĪpproaching this value here. You could say the limit of g of x as x approaches, not x equals, as x approaches, one, what would that be? Pause the video and try to figure it out. But you could take the limit on an infinite number of points for this function right over here. So for example, x approaches five, five is interesting right over here because we have this point discontinuity. Oftentimes we're asked to find the limits as x approaches some type Now another thing to appreciate is for a given function, and let me delete these. So notice, all of these, all of these functionsĪs x approaches five, they all have the limit defined and it's equal to negative six, but these functions all look Greater than or equal to four and it just goes right Maybe it's not defined atĪll for any of these values, and then maybe down here it is defined for all x values You could have a function like this, maybe it's defined up to there, then it's you have a circle there, and then it keeps going. You could have a function like this, let's say the limit, let's call it h of x, as x approaches five is equal to negative six. As we approach from the right, we approaching negative six. As we approach from the left, we're approaching negative six. So for example, a function that looks like this, so let me draw f of x, an f of x that looks like this, and is even defined right over there, and then does something like this. The behavior of the function as x approaches five from both sides, from the left and the right, it has to be approaching negative six. ![]() If you can so the same, if you have some graph paper, In fact if you're up for it, pause this video and see For example, I could say the limit of f of x as x approaches five is equal to negative six, and I can construct anį of x that does this that looks very different than g of x. Many different functions for which the limit as x approaches five is equal to negative six, and they would look veryĭifferent from g of x. What's happening at that point, what g of five is, and it doesn't tell us much about the rest of the function, about the rest of the graph. The behavior of a function as it approaches a point. ![]() But the whole point of this video is to appreciate all that a limit does. ![]() And it's worth noting that that's not what g of five is. So a reasonable estimateīased on looking at this graph is that as x approaches five, g of x is approaching negative six. As x approaches five from the right, g of x looks like it'sĪpproaching negative six. Let's think about what g of x approaches as x approaches five from the left. And I wanna think about what is the limit as x approaches five of g of x? Well we've done this multiple times. So we have the graph of y is equal to g of x right over here. ![]()
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