displaystyle lim x arrow ∞((x2+1/x+1)-a x-b),(a, b ∈ R)=0 text . Then

Question

displaystyle lim x arrow ∞((x2+1/x+1)-a x-b),(a, b ∈ R)=0 text . Then  (A) =0, b=1 (B) a=1, b=-1 (C) a=-1, b-1 (D) a=0, b=0

Tardigrade Admin · Accepted Answer

displaystyle lim x arrow ∞ (x2+1-a x(x+1)-b(x+1)/x+1)=0 = displaystyle lim x arrow ∞ ((1-a) x2-(a+b) x+1-b/x+1)=0 for the limit to exist, 1-a=0 text and -(a+b)=0 ∴ a=1, b=-1

Q. $x \to \infty lim (\frac{x ^{2} + 1}{x + 1} - a x - b), (a, b \in R) = 0 . Then$

=0, b=1$

$a = 1, b = - 1$

$a = - 1, b - 1$

$a = 0, b = 0$

$x \to \infty lim \frac{x ^{2} + 1 - a x ( x + 1 ) - b ( x + 1 )}{x + 1} = 0$
$= x \to \infty lim \frac{( 1 - a ) x ^{2} - ( a + b ) x + 1 - b}{x + 1} = 0$
for the limit to exist,
$1 - a = 0 and - (a + b) = 0$
$∴ a = 1, b = - 1$

Q. x→∞lim​(x+1x2+1​−ax−b),(a,b∈R)=0. Then

=0, b=1$

a=1,b=−1

a=−1,b−1

a=0,b=0

x→∞lim​x+1x2+1−ax(x+1)−b(x+1)​=0 =x→∞lim​x+1(1−a)x2−(a+b)x+1−b​=0 for the limit to exist, 1−a=0 and −(a+b)=0 ∴a=1,b=−1

Q. $x \to \infty lim (\frac{x ^{2} + 1}{x + 1} - a x - b), (a, b \in R) = 0 . Then$

$a = 1, b = - 1$

$a = - 1, b - 1$

$a = 0, b = 0$

$x \to \infty lim \frac{x ^{2} + 1 - a x ( x + 1 ) - b ( x + 1 )}{x + 1} = 0$
$= x \to \infty lim \frac{( 1 - a ) x ^{2} - ( a + b ) x + 1 - b}{x + 1} = 0$
for the limit to exist,
$1 - a = 0 and - (a + b) = 0$
$∴ a = 1, b = - 1$