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

JEE MATHEMATICS MCQ: LIMITS

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Understanding +4 | -1

The value of

\lim\limits_{x \to \infty } \left( {\frac{{{x^2} + bx + 4}}{{{x^2} + ax + 5}}} \right)

View answer and explanation

Correct option: C

Option C (1) is correct because as x approaches infinity, the highest power terms dominate, and the ratio of the coefficients of x² in the numerator and denominator is 1.

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\lim\limits_{h \to 0} 2\left\{ {\frac{{\sqrt 3 \sin \left( {\frac{\pi }{6} + h} \right) - \cos \left( {\frac{\pi }{6} + h} \right)}}{{\sqrt 3 h\left( {\sqrt 3 \cos \,h - \sin \,h} \right)}}} \right\}

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equals