displaystyle limx → ∞ ( (2x -3)(3x -4)/(4x - 5)(5x - 6)) is equal to:

Question

displaystyle limx → ∞ ( (2x -3)(3x -4)/(4x - 5)(5x - 6)) is equal to: (A)  (1/10) (B) 0 (C)  (1/5) (D)  (3/10)

Tardigrade Admin · Accepted Answer

Let f(x) = ( (2x -3)(3x -4)/(4x - 5)(5x - 6)) we have to find displaystyle limx → ∞ f(x) Put x = (1/h), if x → ∞ ,h → 0 then displaystyle limx → ∞ f(x) = displaystyle limh → 0 ( (2x -3h)(3x -4h)/(4x - 5h)(5x - 6h)) = (6/20) = (3/10)

Q. $x \to \infty lim \frac{( 2 x - 3 ) ( 3 x - 4 )}{( 4 x - 5 ) ( 5 x - 6 )}$ is equal to:

$\frac{1}{10}$

0

$\frac{1}{5}$

$\frac{3}{10}$

Let $f (x) = \frac{( 2 x - 3 ) ( 3 x - 4 )}{( 4 x - 5 ) ( 5 x - 6 )}$
we have to find $x \to \infty lim f (x)$
Put $x = \frac{1}{h},$ if $x \to \infty, h \to 0$ then
$x \to \infty lim f (x) = h \to 0 lim \frac{( 2 x - 3 h ) ( 3 x - 4 h )}{( 4 x - 5 h ) ( 5 x - 6 h )}$
$= \frac{6}{20} = \frac{3}{10}$

Q. x→∞lim​(4x−5)(5x−6)(2x−3)(3x−4)​ is equal to:

101​

0

51​

103​

Let f(x)=(4x−5)(5x−6)(2x−3)(3x−4)​ we have to find x→∞lim​f(x) Put x=h1​, if x→∞,h→0 then x→∞lim​f(x)=h→0lim​(4x−5h)(5x−6h)(2x−3h)(3x−4h)​ =206​=103​

Q. $x \to \infty lim \frac{( 2 x - 3 ) ( 3 x - 4 )}{( 4 x - 5 ) ( 5 x - 6 )}$ is equal to:

$\frac{1}{10}$

$\frac{1}{5}$

$\frac{3}{10}$