Question
Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow{\infty}}\frac{5\text{x}^3-6}{\sqrt{9+4\text{x}^6}}$
$\lim\limits_{\text{x}\rightarrow{\infty}}\frac{5\text{x}^3-6}{\sqrt{9+4\text{x}^6}}$
$=\lim\limits_{\text{x}\rightarrow{\infty}}\frac{5-\frac{6}{\text{x}^3}}{\sqrt{\frac{9}{\text{x}^6}+\frac{4\text{x}^6}{\text{x}^6}}}$
$=\lim\limits_{\text{x}\rightarrow{\infty}}\frac{\Big(5-\frac{6}{\text{x}^3}\Big)}{\sqrt{\frac{9}{\text{x}^6}+4}}$
$=\frac{5}{\sqrt{4}}=\frac52$
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If 3rd, 4th, 5th and 6th terms in the expansion of be $(\text{x}+\text{a})^{\text{n}}$ respectively a, b, c and d. prove that $\frac{\text{b}^{2}-\text{ac}}{\text{c}^{2}-\text{bd}}=\frac{5\text{a}}{3\text{c}}.$
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| Number of Girls | 6 | 8 | 14 | 16 | 4 | 2 |