Question

If $f\left(x\right)=\frac{3x+7}{6x+4}$ what value does $f\left(x\right)$ approach as $x$ gets infinitely larger?

• A. $0$
• B. $1/2$
• C. $3/4$
• D. $7/4$
• E. Infinity

Answer 1

The correct option is B $1/2$

$\underset{x\to \infty }{lim}f\left(x\right)=\underset{x\to \infty }{lim}\frac{x}{x}\left(\frac{3+\frac{7}{x}}{6+\frac{4}{x}}\right)$

$=\frac{3+0}{6+0}=\frac{1}{2}$ $(asx\to \infty ;\frac{1}{x}\to 0)$