# Which Limit Law should I refer to in my solution?

by Abuda
Tags: limit, refer, solution
 P: 7 1. The problem statement, all variables and given/known data Evaluate the limit below indicating the appropriate Limit Law(s) implemented. $$\lim_{x\rightarrow 0.5}\frac{2x^2+5x-3}{6x^2-7x+2}[/itex] 2. The attempt at a solution [tex]\lim_{x\rightarrow 0.5}\frac{2x^2+5x-3}{6x^2-7x+2}=\lim_{x\rightarrow 0.5}\frac{2(x-0.5)(x+3)}{6(x-0.5)(x-(2/3))}=\lim_{x\rightarrow 0.5}\frac{2(x+3)}{6(x-(2/3))}=-7[/itex] So would I be required to state anything when I can out the (x-0.5) factor? (PS, I'm doing Real Analysis and have learnt about proving limits from first principles but I'm now trying to learn about using shortcuts by referencing theorems.) HW Helper Thanks P: 10,627  Quote by Abuda 1. The problem statement, all variables and given/known data Evaluate the limit below indicating the appropriate Limit Law(s) implemented. [tex]\lim_{x\rightarrow 0.5}\frac{2x^2+5x-3}{6x^2-7x+2}$$ 2. The attempt at a solution $$\lim_{x\rightarrow 0.5}\frac{2x^2+5x-3}{6x^2-7x+2}=\lim_{x\rightarrow 0.5}\frac{2(x-0.5)(x+3)}{6(x-0.5)(x-(2/3))}=\lim_{x\rightarrow 0.5}\frac{2(x+3)}{6(x-(2/3))}=-7$$ So would I be required to state anything when I can out the (x-0.5) factor? (PS, I'm doing Real Analysis and have learnt about proving limits from first principles but I'm now trying to learn about using shortcuts by referencing theorems.)