I am going over my test and I am not sure what I was supposed to do for this question.
$ \lim_{x \to -\infty} \frac {\sqrt {x^2 + 3x}}{3-2x}$
I attempted to do the algebra but my algebra skills are too weak to do it so I resorted to logic. I stated that the top will reduce to a positive x and the bottom will reduce to a positive $2x$ giving $ \frac {x}{2x}$ which will then give me $1/2$ but this answer is wrong. Apparently the answer is correct but my reasoning is wrong.
I don't know why it is wrong but it is incredibly frustrating to me that I can get the correct answer with logical conclusions but still get the question on the test wrong. This is my second time taking calculus and at this rate I am going to fail again, no matter how hard I try I just can't get it right for some reason.
I guess this could be a broader question, but how do you take a math test? It is a mystery to me and I have absolutely no idea what a teacher expects on tests. They showed us this method in class, but on a test it is incorrect. To further complicate things I got the epsilon delta problem wrong because I didn't show the absolute value and all that stuff at the start even though I was able to show the correct epsilon.