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3 ways to find limits in calculus11/22/2023 Informally people will say oh it's approaching infinity The right hand side it looks like the same thing is happening we're going unbounded to infinity. Unbounded towards infinity and as we approach from It looks like we're going unbounded as x goes. Well we'll do the same thing, from the left hand side, If the limit of g of x as x approaches seven. There but the g of seven is different than the value Is going to be equal to two and so once again, theįunction is defined there and the limit exists We are approaching two and so I would say that this Seems like the same thing is happening it seems like We approach x equals seven from the right hand side it Value of our function is approaching two, it doesn't matter that the actual function isĭefined g of seven is five but as we approach from the left, as x goes 6.9, 6.99 and so on, it looks like our value of our function is approaching two, and as Seven 6.9, 6.99, 6.999 well it looks like the What happens as we approach from the left from values less than Now let's think about the limit of g of x as x approaches seven so Just looking at this graph but it looks like a value When looking at a graph it's not that precise so I would say it's approximately 0.4 it might be 0.41 it might be 0.41456789 we don't know exactly So I'll say this limit definitely exists just And so this value, justĮye balling it off of here looks like it's about. Straight Line that takes us so it looks like we'reĪpproaching this value and as we approach fiveįrom the right hand side it also looks like we areĪpproaching that same value. Limit as x approaches five g of x so as we approachįive from the left hand side it looks like we areĪpproaching this value let me just draw a Video and have a go at it and see if you can figure Of Y is equal to g of x and once again pause this Just to get more cases of looking at graphical limits. The value of the function at x equals six, here theįunction was not defined at x equals four, but the limit does exist here the function is definedĪt f equals, x equals two but the limit does not existĪs we approach x equals two let's do another function In this first case theįunction is defined at six and the limit is equal to Would say that this limit does not exist so does not exist. Getting closer and closer to five and since we areĪpproaching two different values from the left hand sideĪnd the right hand side as x approached twoįrom the left hand side and the right hand side we It looks like our function the value of our function's To five but as we go from you know 2.1 2.01 2.001 Two from the right hand side, our function is gettingĬloser and closer to five it's not quite getting It looks like our function is approaching the value of two but when we approachįrom the right hand side, when we approach x equals See when we approach from the left hand side So this is interesting theįunction is defined there f of two is two, let's Least from what we can tell from the graph it looks like the limit of f of x is x approaches four is three, even though the function Limit exist at an x value where the function itself is not defined, the function, if you saidĪfter four, it's not defined but it looks like when weĪpproach it from the left when we approach xĮquals four from the left it looks like f is approaching three and then we approach four from the right, once again, it looks like ourįunction is approaching three so here I would say, at The value of our function it looks like it is approaching three. The limit of f of x is x approaches four so as we approach fourįrom the left hand side what is going on? Well as we approach fourįrom the left hand side it looks like our function, Like we are approaching one right over there, in a darker color. With a graph but this is a pretty good estimate, it looks Once again approaching one and in order for this limit to exist, we need to be approaching the same value from both the left and the right hand side and so here at least graphically, so you never are sure Six from the right hand side it looks like our f of x is X is approaching one and as we approach x equals In a color you can see, as x approaches six from both sides well as we approach sixįrom the left hand side, from values less than six, it looks like our f of Think about what's the limit of f of x it's x approaches six. If you can figure it out on your own before we do it together. The graph of Y equals f of x right over here and we want to figure out three different limits and like always pause this video and see
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