The value of mathop {lim }limits_{x to infty | vedclass

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(B) To find the limit $\mathop {\lim }\limits_{x 	o \infty } \left( {\frac{{{x^2} + bx + 4}}{{{x^2} + ax + 5}}} ight)$,divide the numerator and the

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$1$

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(B) To find the limit $\mathop {\lim }\limits_{x 	o \infty } \left( {\frac{{{x^2} + bx + 4}}{{{x^2} + ax + 5}}} ight)$,divide the numerator and the denominator by $x^2$: $\mathop {\lim }\limits_{x 	o \infty } \left( {\frac{{1 + \frac{b}{x} + \frac{4}{{{x^2}}}}}{{1 + \frac{a}{x} + \frac{5}{{{x^2}}}}}} ight)$ As $x 	o \infty$,the terms $\frac{b}{x}$,$\frac{4}{x^2}$,$\frac{a}{x}$,and $\frac{5}{x^2}$ all approach $0$. Therefore,the limit is $\frac{1 + 0 + 0}{1 + 0 + 0} = 1$.

The value of $\mathop {\lim }\limits_{x \to \infty } \left( {\frac{{{x^2} + bx + 4}}{{{x^2} + ax + 5}}} \right)$ is

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