6. `lim_(xto1)(1-x^2)^(1/log(1-x))`

If l=lim_(xto1^(+))2^(-2^(1/(1-x))) and m=lim_(xto1^(+))(x sin (x-[x]))/(x-1) (where [.] denotes greatest integer function). Then (l+m) is ………….

Evalate lim_(xto1^(+)) 2^(-2^((1)/(1-x))).

Evaluate lim_(xto1) ((2)/(1-x^(2))-(1)/(1-x)).

Find the following limits: (i) lim_(xto0) (1-x)^((1)/(x))" "(ii) lim_(xto1) (1+log_(e)x)^((1)/(log_(e)x)) (iii)lim_(xto0) (1+sinx)^((1)/(x))

Evalaute lim_(xto1) (1+logx-x)/(1-2x+x^(2))

The value of lim_(xto0) (1+sinx-cosx+log(1-x))/(x^(3)) is

lim_(x->1) (1-x^2) ^ frac{1}{log(1-x)}

lim_(xto0) (log(1+x+x^(2))+log(1-x+x^(2)))/(secx-cosx)=

Evaluate x lim_(xto2) (x-2)/(log_(a)(x-1)).

Number of integral values of k for which lim_(xto1) sin^(-1)((k)/(log_(e)x)-(k)/(x-1)) exists is _________.