Find the limit of the function algebraically (with cancellation techniques and direct substitution, that is, since this is in indeterminate form): [tex]\lim_{x \to 0} \frac{x^2+3}{x^4} [/tex]------It seems to have a dividing by zero issue from what I have managed to get out of the problem... That or I am having trouble discerning how to break it down into a manageable 0 issue. Help would be greatly appreciated, or at the very least a confirmation that I have the correct answer in that there is no limit.
Accepted Solution
A:
At x=0, the numerator is positive and the denominator is zero. The form is not "indeterminate", but is "undefined". The limit is the same (+β) whether approaching zero from the left or the right, so we say
Β the limit is +β
_____ The case of "no limit" is reserved for those conditions in which the value you get approching from the left is different from that approaching from the right and/or is different from the defined value of the function at the point.
For example, 1/x has no limit at x=0 because it approaches -β from the left and +β from the right.