This is more of a conceptual question dealing with a homework problem than with the problem itself... So I am asked to find various limits for the function (x2-9x+8)/(x3-6x2). All well, no problems... I am asked to find the left and right hand limits as x→0, which is -∞ for each. At the end of the problem I am asked to either state the limit as x→0 or state that the limit does not exist. Here is where I have a question. When a one-sided limit is either positive or negative infinity, the limit does not exist. When the equations for the one-sided limits are written, they are not stating that the limits exists but rather using it as a convenient description of the function's behavior near that value of x and as an explanation for why the one-sided limit does not exist. *I base this off of what it says in my text* However, if the one-sided limits at that point both go to either positive or negative inifinity, then the normal limit exists and L= +/-∞. I'm having trouble grasping why the one sided limits do not exist when the function values approach infinity but the normal limit does exist when each of the one sided limits approach infinity. I can understand why we can say that the limit is infinity as a description of the function's behavior even though this limit does not actually exist. However, why is it wrong to say that this limit does not exist?