Find the limit of the function algebraically (with cancellation techniques and direct substitution, that is, since this is in indeterminate form): it seems to have a dividing by zero issue from what i have managed to get out of the that or i am having trouble discerning how to break it down into a manageable 0 issue. would be greatly appreciated, or at the very least a confirmation that i have the correct answer in that there is no limit.

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 (+∞) whether approaching zero from the left or the right, so we say

  the limit is +∞


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 -∞ from the left and +∞ from the right.