I do not understand how absolute value effects this, and why is what I have done wrong. Is the way I tackled the problem correct or am I totally wrong?
I have looked at this post limits, but the definition of absolute value I dont get, I thought |-2|=2, the same would |-x|=x. What am I not getting?
Best Answer
Suppose you didn't know whether $x$ is positive or negative, then how will you analyse the expression $\Large \frac{2x-5}{|3x+2|}$?
You will have to consider two cases:
(1)If $x$ is positive, then $\Large \frac{2x-5}{|3x+2|}=\Large \frac{2x-5}{3x+2}$
(2)If $x$ is negative, then $\Large \frac{2x-5}{|3x+2|}=\Large \frac{2x-5}{-(3x)+2}$
But in your example, we are given that $x\rightarrow-\infty$
Since $x\rightarrow-\infty$, what you are doing is, dividing numerator by negative value, which is $x$ and denominator by positive value, which is $|x|$.