Evaluate the given limit: mathop {lim }limits | vedclass

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Question

(A) To evaluate the limit $\mathop {\lim }\limits_{x 	o 1} \frac{a x^{2}+b x+c}{c x^{2}+b x+a}$,we substitute $x = 1$ directly into the expression si

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$1$

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(A) To evaluate the limit $\mathop {\lim }\limits_{x 	o 1} \frac{a x^{2}+b x+c}{c x^{2}+b x+a}$,we substitute $x = 1$ directly into the expression since the denominator is not zero at $x = 1$ (given $a+b+c 
eq 0$).$\mathop {\lim }\limits_{x 	o 1} \frac{a x^{2}+b x+c}{c x^{2}+b x+a} = \frac{a(1)^{2}+b(1)+c}{c(1)^{2}+b(1)+a}$$= \frac{a+b+c}{c+b+a}$Since $a+b+c 
eq 0$,we can cancel the numerator and the denominator.$= 1$

Evaluate the given limit: $\mathop {\lim }\limits_{x \to 1} \frac{a x^{2}+b x+c}{c x^{2}+b x+a}$,where $a+b+c \neq 0$.

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