Lim_(x->∞)(7x^2+2x+11)/(6x^4-2x)=? 

প্রশ্ন: \( \lim_{x \to \infty} \frac{7x^2 + 2x + 11}{6x^4 - 2x} = ? \)

সমাধান:

আমরা \(x^4\) দিয়ে লব এবং হরকে ভাগ করি:

\( \lim_{x \to \infty} \frac{\frac{7x^2}{x^4} + \frac{2x}{x^4} + \frac{11}{x^4}}{\frac{6x^4}{x^4} - \frac{2x}{x^4}} \)

\( = \lim_{x \to \infty} \frac{\frac{7}{x^2} + \frac{2}{x^3} + \frac{11}{x^4}}{6 - \frac{2}{x^3}} \)

এখন, \(x \to \infty\) হলে, \( \frac{7}{x^2} \to 0 \), \( \frac{2}{x^3} \to 0 \) এবং \( \frac{11}{x^4} \to 0 \) এবং \( \frac{2}{x^3} \to 0 \) হয়। সুতরাং,

\( = \frac{0 + 0 + 0}{6 - 0} \)

\( = \frac{0}{6} \)

\( = 0 \)

সুতরাং, \( \lim_{x \to \infty} \frac{7x^2 + 2x + 11}{6x^4 - 2x} = 0 \) 🎉