Cast your mind back to the year 2004, a very fetch year. The following limit was in the climax to the popular film Mean Girls (sure there was very interesting comedy about high school life and fitting in, but the climax of the film was definitely the math competition). By carefully showing your work, resolve this limit:

I used L'Hopital's Rule to find what the derivative of the numerator and the denominator are. I know the answer is the limit DNE, and I know this is because the left and right side limits approach different values (positive infinity and negative infinity, respectively). I am just not sure how to solve this ALGEBRAICALLY.