The value of displaystyle limx → 0 (|3x2 + 1|/2x2 + 1) is :

Question

The value of displaystyle limx → 0 (|3x2 + 1|/2x2 + 1) is : (A)  (3/2) (B)  (2/3) (C) - (3/2) (D)  - (2/3)

Tardigrade Admin · Accepted Answer

Consider displaystyle limx → 0 (|3x2 + 1|/2x2 + 1) = displaystyle limx→0 (3x2 +1/2x2 +1) = displaystyle lim x→ 0 (x2(3 + (1/x2))/x2 (2+ (1)x2)) = displaystyle lim x→ 0 (3+1 /x2/2+1 /x2) = (3+0/2+0) =(3/2)

Q. The value of $x \to 0 lim \frac{∣3 x ^{2} + 1∣}{2 x ^{2} + 1}$ is :

$\frac{3}{2}$

$\frac{2}{3}$

$- \frac{3}{2}$

$- \frac{2}{3}$

Consider $x \to 0 lim \frac{∣3 x ^{2} + 1∣}{2 x ^{2} + 1}$
$= x \to 0 lim \frac{3 x ^{2} + 1}{2 x ^{2} + 1} = x \to 0 lim \frac{x ^{2} ( 3 + \frac{1}{x ^{2}} )}{x ^{2} ( 2 + \frac{1}{x ^{2}} )}$
$= x \to 0 lim \frac{3 + 1/ x ^{2}}{2 + 1/ x ^{2}} = \frac{3 + 0}{2 + 0} = \frac{3}{2}$

Q. The value of x→0lim​2x2+1∣3x2+1∣​ is :

23​

32​

−23​

−32​