`lim_(x-gt0)(2^(x-1)+1/2)^(1/ x)`

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

lim_(x to 0) (2^(x) - 1)/(sqrt(1 + x) - 1) =

lim_(x to 0) (2^(x) - 1)/(sqrt(1 + x) - 1) =

Use formula lim_(x rarr0)(a^(x)-1)/(x)=log(a) to find lim_(x rarr0)(2^(x)-1)/((1+x)^((1)/(2))-1)

lim_(x->0) (x^2-3x+1)/(x-1)

Statement-1 : lim_(x to 0) (1 - cos x)/(x(2^(x) - 1)) = (1)/(2) log_(2) e . Statement : lim_(x to 0) ("sin" x)/(x) = 1 , lim_(x to 0) (a^(x) - 1)/(x) = log a, a gt 0

Statement-1 : lim_(x to 0) (1 - cos x)/(x(2^(x) - 1)) = (1)/(2) log_(2) e . Statement : lim_(x to 0) ("sin" x)/(x) = 1 , lim_(x to 0) (a^(x) - 1)/(x) = log a, a gt 0

lim_ (x-> 0) (log (a + x) -loga) / x + klim_ (x-> e) (logx-1) / (xe) = 1 then

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)