Always remember that you need to keep track of the conditions that make the denominator of an algebraic expression equal to zero. Even though you can’t evaluate an expression when you’re dividing by zero, you can however calculate an expression when the denominator is close (think a decimal with a lot of zeros) to zero. As usual, limits are extremely helpful when you’re dealing with an equation where you might be dividing by zero.
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I understand the limit is negative infinity and positive infinity for this function, but I don't quite understand how he chose the numbers -2.999+8 and -2.999-2. I get confused when finding the limits as he chooses these numbers. I think this video would be helpful if you understand what he is trying to do.
This pencast helps in showing how to evaluate the one-sided limit, but I I do not think that this was the best example. It makes sense in that the limit is negative infinity for one side of the function and positive infinity for the other, but how can a limit be infinity? Infinity isn't a real number and I thought that a limit had to approach an actual numerical value. As this function approaches -3 I will agree that the function goes to infinity from the left and negative infinity from the right, but I don't necessarily agree that you can call that the limit. I just don't understand how a limit can be infinity.