The integer `n` for which `lim_(x->0)((cosx-1)(cosx-e^x))/(x^n)` is finite nonzero number is ________

Find the integral value of n for which lim_(x->0)(cos^2x-cosx-e^xcosx+e^x-(x^3)/2)/(x^n) is a finite nonzero number

lim_(xto0)(1-cos(1-cosx))/(x^(4)) is

lim_(xto0) ((1-cos2x)(3+cosx))/(xtan4x) is equal to

lim_(xto0)(1-cosx)/x^(2)

lim_(xto0)(e^(x^(2))-cosx)/(x^(2))=

lim_(xto0)(sinx(1-cosx))/x^(3)

If lim_(xrarr0) (e^(ax)-e^(x)-x)/(x^(2))=b (finite), then

lim_(xto pi/2)(2x-pi)/cosx

Evaluate lim_(xto0) (1-cos(1-cosx))/(x^(4)).

The value of lim_(xto0) (1-(cosx)sqrt(cos2x))/(x^(2)) is