The value of displaystyle limx → ∞ √a2x2+ax+1-√a2x2+1 is

Question

The value of displaystyle limx → ∞ √a2x2+ax+1-√a2x2+1 is (A) (1/2) (B) 1 (C) 2 (D) None of these

Tardigrade Admin · Accepted Answer

Given displaystyle limx → ∞ √a2x2+ax+1-√a2x2+1 = displaystyle limx → ∞ (a2x2+ax+1-a2x2-1/√a2x2+ax+1+√a2x2+1) = displaystyle limx → ∞ (ax/x[√a2+(a)x+(1)x2+√a2+(1/x2)] =(a/√a2+√a2)=(a/2a) =(1/2)

Q. The value of $x \to \infty lim$ $a^{2} x^{2} + a x + 1 - a^{2} x^{2} + 1$ is

$\frac{1}{2}$

$1$

$2$

None of these

Q. The value of x→∞lim​ a2x2+ax+1​−a2x2+1​ is

21​

1

2

None of these

Given x→∞lim​ a2x2+ax+1​−a2x2+1​ =x→∞lim​ a2x2+ax+1​+a2x2+1​a2x2+ax+1−a2x2−1​ =x→∞lim​ x[a2+xa​+x21​​+a2+x21​​]ax​ =a2​+a2​a​=2aa​ =21​

Q. The value of $x \to \infty lim$ $a^{2} x^{2} + a x + 1 - a^{2} x^{2} + 1$ is

$\frac{1}{2}$

$1$

$2$