Question
Evaluate $\mathop {\lim }\limits_{x \to 1} \frac{{a{x^2} + bx + c}}{{c{x^2} + bx + a}},\;a + b + c \ne 0$
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Answer
Here $\mathop {\lim }\limits_{x \to 1} \frac{{a{x^2} + bx + c}}{{c{x^2} + bx + a}}$
$ = \frac{{a \times {{(1)}^2} + b \times 1 + c}}{{c \times {{(1)}^2} + b \times 1 + a}} = \frac{{a + b + c}}{{c + b + a}} = 1$
$ = \frac{{a \times {{(1)}^2} + b \times 1 + c}}{{c \times {{(1)}^2} + b \times 1 + a}} = \frac{{a + b + c}}{{c + b + a}} = 1$
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