This is approaching the three from values larger than three. So these aren't negative values, these are just approaching the three right over here from Value that you're trying to find the limit at. The limit from the left are to the left of the x The limit from the right are positive values. Or the limit from the right, they imagine that the limit from the left is negative values and The limit from both sides, or the limit from the left What these are going to be, sometimes when people say Now one key idea here to point out, before I even calculate So let's get a calculator out and do this. And every time we getĬloser and closer to three, we're gonna get a betterĪpproximation for, or we're gonna get a better sense of what we are actually approaching. Get a little bit closer, we could go three point zero one. So we could say three point one, but then we might wanna Those would be x values larger than three. And so what values would those be? Well those would be, So we could also try to approximate the limit from the right. But we also, in orderįor the limit to exist, we have to be approaching the We're moving to the right, but these are the x values that are on the left side of three, This on a coordinate plane, these are the x values thatĪre to the left of three, but we're getting closerĪnd closer and closer. Now why do I say the left? Well if you think about What this expression equals as we get closer and closer to three, we're trying to approximate And so one way to think about it here is as we try to figure out And then we could goĮven closer than that. But then we can try to getĮven a little bit closer than that, we could go Go to two point nine and figure out what the expression equals when x is two point nine. Gonna, let's try out x values that get closer and closer The reason why I set up two tables, I didn't have to do two tables, I could have done it all in one table, but hopefully this will make it a little bit more intuitive This is x to the third minus three x squared over five x minus 15. So this is x and this is x to the third minus three x squared over five x minus 15. And to do that, I'm gonna set up a table. But let's see, even though the function, or even though theĮxpression is not defined, let's see if we can get a sense We get this indeterminate form, we get zero over zero. So this expression is actually not defined at x equals three. So at x equals three, thisĮxpression's gonna be, let's see in the numerator Three to the third power minus three times three squared, over five times three minus 15. Might wanna try out is, well what happens to this expression when x is equal to three? Well then it's going to be We get as x gets closer and closer to three. Now when I say get a sense, we're gonna do that by seeing what values for this expression This video we're going to try to get a sense of what the limitĪs x approaches three of x to the third minus three x squared over five x minus 15 is. Also make sure you are including the decimal point for each instance of x in the function. If you are still getting answers far from the limit value of 1.8 on your calculator, check that you are using the same number of 9's (or same number of 0's) after the decimal point for each instance of x in the function. It is much preferable to use a calculator that performs standard order of operations.Įxample on a TI-89 calculator that performs standard order of operations, for x = 2.999: For example, if you type 5 + 2 * 3, your calculator performs standard order of operations if it displays 11, but does not do this if it displays 21. Make sure to include parentheses around the expression in the numerator and parentheses around the expression in the denominator, so that the calculator divides these entire expressions.Īlso, you should test whether your calculator performs the standard order of operations. radian mode would have been an issue had the calculation involved a trigonometric function). Calculator mode is not an issue here for this type of calculation (but degree mode vs. Probably the most common error for this type of calculation is to enter the expression incorrectly, so that the calculator performs the operations in the wrong order. Without seeing your calculator keystrokes, I don't know for sure what error you are making.
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