Limits Continuity And Differentiability

Consider the following statements

Statement 1 : \(\lim _\limits{x \rightarrow 1} \frac{a x^2+b x+c}{x^2+b x+a}\) is 1

(where \(a+b+c \neq 0\)).

Statement 2 : \(\lim _\limits{x \rightarrow -2} \frac{\frac{1}{x}+\frac{1}{2}}{x+2}\) is \(\frac{1}{4}\).