My question is about the type of approach when evaluating the limit as x approaches infinity versus the limit as x approaches a. I understand that L's Rule is used to evaluate indeterminate forms such as 0/0 and infinity/infinity.
For example, lim as x approaches 1 (x^2 - 1)/(x^2 - x) can be factored and evaluated to 2, but what about something like lim as x approaches 1/2 (6x^2 + 5x - 4)/(4x^2 + 16x - 9)?
I get 0/0, which is an indeterminate. I then find the derivative which is (12x+5)/(8x+16) = 11/20. Is this the right thinking or right methodology? The first time I did the problem, I evaluated it down to 3/2, but that was after the second derivative. I'm thinking that's over kill. What do you think?
These problems are for homework. Feel free to post any problems that you think might help me with this tool. By the way, I'll post more questions concerning evaluating an expression as x approaches infinity in the near future. I'm sure I'll have some questions.
Thanks for your help. I appreciate it.