Question

$\underset{x\to \infty }{lim}{\left(\frac{3x^2+2x+1}{x^2+x+2}\right)}^{\frac{6x+1}{3x+2}}\text{is equal to}$

• A. 3
• B. 9
• C. 1
• D. 4

Answer 1

The correct option is B

9

$\underset{x\to \infty }{lim}{\left(\frac{3x^2+2x+1}{x^2+x+2}\right)}^{\frac{6x+1}{3x+2}}\underset{x\to \infty }{lim}{\left(\frac{3+\frac{2}{x}+\frac{1}{x^2}}{1+\frac{1}{x}+\frac{2}{x^2}}\right)}^{\frac{6+\frac{1}{3}}{3+\frac{2}{x}}}={\left(\frac{3}{1}\right)}^{6/3}=9$