Question

$\underset{x\to \infty }{lim}\frac{\sqrt{1+25x^2}+\sqrt{9x^2-1}}{\sqrt{1+25x^2}-\sqrt{9x^2-1}}=$

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is D $4$

$li{m}_{x\to \infty }\frac{\sqrt{1+25x^2}+\sqrt{9x^2-1}}{\sqrt{1+25x^2}-\sqrt{9x^2-1}}$

$=li{m}_{x\to \infty }\frac{x\sqrt{1/x^2+25}+x\sqrt{9-1/x^2}}{x\sqrt{1/x^3+25}-x\sqrt{9-1/x^2}}=li{m}_{x\to \infty }\frac{\sqrt{9-0}}{\sqrt{25}-\sqrt{9-0}}=\frac{\sqrt{25}+\sqrt{9}}{\sqrt{25}-\sqrt{9}}$

$=\frac{5+3}{5-3}=\frac{8}{2}=4$