([ti),L_(t)],[x rarr(5)/(2),(x]]

lim_(x rarr0)(2^(5x)-1)/(x)

lim_(x rarr0)(1+2x)^(5/x)

L_(1)=lim_(x rarr0^+)(1+x)^(1/x),L_(2)=lim_(x rarr0^(+))(1+x)^(1/x^(2)),L_(3)=lim_(x rarr0^(+))(1+x^(2))^(1/x) ,Then

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 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

The value of lim_(x rarr0)x^(2)[(1)/(x^(2))] where [.] denotes G.L.F.is

Plot the graph of the function f(x)=lim_(t rarr0)((2x)/(pi)(tan^(-1)x)/(t^(2)))

Let L_(1)=lim_(x rarr4)(x-6)^(x)ndL_(2)=lim_(x rarr4)(x-6)^(4) Which of the following is true? Both L_(1) and L_(2) exists Neither L_(1) and L_(2) exists L_(1) exists but L_(2) does not exist L_(2) exists but L_(1) does not exist

lim_(x rarr0)((1+5x^(2))/(1+3x^(2)))^(1/x^(2))=

lim_(x rarr0)((5x^(2)+1)/(3x^(2)+1))^(1/x^(2))