Consider the following statements:Statement 1 | vedclass

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(B) For Statement $1$:$\lim _{x \rightarrow 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}{a+b+c} = 1

Vedclass · Accepted Answer

Only statement $1$ is true.

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(B) For Statement $1$:$\lim _{x ightarrow 1} \frac{a x^{2}+b x+c}{c x^{2}+b x+a} = \frac{a(1)^{2}+b(1)+c}{c(1)^{2}+b(1)+a} = \frac{a+b+c}{a+b+c} = 1$.Since $a+b+c 
eq 0$,the limit is $1$. Thus,Statement $1$ is true.For Statement $2$:$\lim _{x ightarrow -2} \frac{\frac{1}{x}+\frac{1}{2}}{x+2} = \lim _{x ightarrow -2} \frac{\frac{2+x}{2x}}{x+2} = \lim _{x ightarrow -2} \frac{2+x}{2x(x+2)} = \lim _{x ightarrow -2} \frac{1}{2x} = \frac{1}{2(-2)} = -\frac{1}{4}$.Since $-\frac{1}{4} 
eq \frac{1}{4}$,Statement $2$ is false.

Consider the following statements:
Statement $1$: $\lim _{x \rightarrow 1} \frac{a x^{2}+b x+c}{c x^{2}+b x+a} = 1$ (where $a+b+c \neq 0$).
Statement $2$: $\lim _{x \rightarrow -2} \frac{\frac{1}{x}+\frac{1}{2}}{x+2} = \frac{1}{4}$.

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Consider the following statements:Statement $1$: $\lim _{x \rightarrow 1} \frac{a x^{2}+b x+c}{c x^{2}+b x+a} = 1$ (where $a+b+c \neq 0$).Statement $2$: $\lim _{x \rightarrow -2} \frac{\frac{1}{x}+\frac{1}{2}}{x+2} = \frac{1}{4}$.