`lim_(x-gt0)(2x)^(3x)=`

lim_(x-gt0) (e^(3x)-1)/(log(1+5x))

lim_(x-gt0)(cos2x-cos3x)/(cos4x-1)

Which of the following is/are true? (a) lim_(x->oo)((2+x)^(40)(4+x)^5)/((2-x)^(45))=1 (b) lim_(x->0)(1-cos^3x)/(xsinxcosx)=3/2 (c) lim_(x->0)(ln(1+2x)-2"ln"(1+x))/(x^2)=-1 (d) lim_(x->oo)(cot^(-1)(sqrt(x+1)-sqrt(x)))/(sec^1((2x+1)/(x-1)^2)=1

lim_(x->0;)(root(3)(1+3x) \ -1-x)/((1+x)^(101)-1-101 x) has the value equal to

Evaluate the limits, if exist lim_(x-gt0)(log_e(1+2x))/(x)

Let f(x)=lim_(n->oo)(2x^(2n)sin(1/x)+x)/(1+x^(2n)) then find (a) lim_(x->oo) xf(x) (b) lim_(x->1) f(x) (c) lim_(x->0) f(x) (d) lim_(x->-oo) f(x)

lim_(x-gt0) (xcot4x)/((cot^2 2x)(sin^2 x)) is equal to (A) 1 (B) 2 (C) 4 (D) 6

If f(x)={x+1/2, x<0 2x+3/4,x >=0 , then [(lim)_(x->0)f(x)]= (where [.] denotes the greatest integer function)

If f(x)={x+1/2, x<0 2x+3/4,x >=0 , then [(lim)_(x->0)f(x)]= (where [.] denotes the greatest integer function)

If x gt0 and g is bounded function then lim_(xtooo)(f(x)e^(nx)+g(x))/(e^(nx)+1)