Find the limit of displaystyle lim x arrow ∞ ((x-5)(x-4)/(2 x-3)(x-7))

Question

Find the limit of displaystyle lim x arrow ∞ ((x-5)(x-4)/(2 x-3)(x-7)) (A) 0 (B) 1 (C) (1/2) (D) -1

Tardigrade Admin · Accepted Answer

displaystyle lim x arrow ∞ ((x-5)(x-4)/(2 x-3)(x-7)) = displaystyle lim x arrow ∞ (x2-9 x+20/2 x2-17 x+21) = displaystyle lim x arrow ∞ (1-(9/x)+(20/x2)/2-(17)x+(21)x2=(1/2)

Q. Find the limit of $x \to \infty lim \frac{( x - 5 ) ( x - 4 )}{( 2 x - 3 ) ( x - 7 )}$

0

1

$\frac{1}{2}$

-1

$x \to \infty lim \frac{( x - 5 ) ( x - 4 )}{( 2 x - 3 ) ( x - 7 )} = x \to \infty lim \frac{x ^{2} - 9 x + 20}{2 x ^{2} - 17 x + 21}$
$= x \to \infty lim \frac{1 - \frac{9}{x} + \frac{20}{x ^{2}}}{2 - \frac{17}{x} + \frac{21}{x ^{2}}} = \frac{1}{2}$

Q. Find the limit of x→∞lim​(2x−3)(x−7)(x−5)(x−4)​

0

1

21​

-1

x→∞lim​(2x−3)(x−7)(x−5)(x−4)​=x→∞lim​2x2−17x+21x2−9x+20​ =x→∞lim​2−x17​+x221​1−x9​+x220​​=21​

Q. Find the limit of $x \to \infty lim \frac{( x - 5 ) ( x - 4 )}{( 2 x - 3 ) ( x - 7 )}$

$\frac{1}{2}$

$x \to \infty lim \frac{( x - 5 ) ( x - 4 )}{( 2 x - 3 ) ( x - 7 )} = x \to \infty lim \frac{x ^{2} - 9 x + 20}{2 x ^{2} - 17 x + 21}$
$= x \to \infty lim \frac{1 - \frac{9}{x} + \frac{20}{x ^{2}}}{2 - \frac{17}{x} + \frac{21}{x ^{2}}} = \frac{1}{2}$