[" Category "A],[" Find "L_(1)(2x^(3))/(3x^(2)+x+2)],[x rarr oo]

lim_(x rarr oo)(x^(2)+3x)/(x^(2)+x+1)

lim_(x rarr oo)(2x+1)/(3x-2)

Evaluate: lim_(x rarr 0) (2^(3x)-1)/(3^(2x)-1)

L_(x rarr1)[(x-1)/(x^(2)-x)-(1)/(x^(3)-3x^(2)+x)]

lim_(x rarr oo)(2+sin x)/(x^(2)+3)

Value of lim_(x rarr oo)((x^(3))/(3x^(2)-4)-(x^(2))/(3x+2)) is

lim_(x rarr oo)((x^(3))/(3x^(2) - 4) - (x^(2))/(3x+2)) is equal to

Let L_(1)=lim_(x rarr0)((sin(2x)+cos(x)-1)/(x)) , L_(2)=lim_(x rarr oo)(sqrt(x^(2)-x)-x) , and L_(3)=lim_(x rarr4)(x^(2)-3x)/(x^(2)-x) , then the value of L_(1)L_(2)+(1)/(L_(3)) is

Let [x] denote the greatest integer not exceeding x. If l_(1) = lim_(x rarr 2^(+)) (x^(2) + [x]), l_(2) = lim_(x rarr 2^(+)) (2x - [x]) and l_(3) = lim_(x rarr (pi)/(2))((cos x)/(x-(pi)/(2))) , then

Let f(x) = underset(n rarr oo)("Lim")( 2x^(2n) sin""(1)/(x) +x)/(1+x^(2n)) then find underset( x rarr -oo)("Lim") f(x)