_ x 2 x^2+3 x+4 3 x^2+3 x+4 = - Vidyadip

MCQ

$\lim _{x \rightarrow \infty} \frac{2 x^2+3 x+4}{3 x^2+3 x+4}=$

A
2
B
3
✓
$\frac{2}{3}$
D
$\frac{3}{2}$

✓

Answer

Correct option: C.

$\frac{2}{3}$

(C)
$\lim _{x \rightarrow \infty} \frac{2 x^2+3 x+4}{3 x^2+3 x+4}=\lim _{x \rightarrow \infty} \frac{2+\frac{3}{x}+\frac{4}{x^2}}{3+\frac{3}{x}+\frac{4}{x^2}}=\frac{2}{3}$
Alternate method:
$\lim _{x \rightarrow \infty}\left(\frac{a x ^ 2+b x+c}{d x ^ 2+e x+f}\right)=\frac{a}{d}$
Here, degree of $N ^{ r }=$ degree of $D ^{ r }$
$\lim _{x \rightarrow \infty} \frac{2 x^2+3 x+4}{3 x^2+3 x+4}=\frac{2}{3}$

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