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

The integer n for which the lim_(x to 0)(cos^(2)x-cosx-e^(x)cosx+e^(x)-(x^(3))/2)/(x^(n)) is a finite non-zero number is

The integer n for which lim_(x rarr0)((cos x-1)(cos x-e^(x)))/(x^(n)) is a finite non- zero number is:

The integer n for which lim_(x rarr0)((cos x-1)(cos x-e^(x)))/(x^(n)) is finite nonzero number is

The least integer n for which lim_(x to 0) ((cos x - 1) (cos x - e^(x)))/(x^(n)) is a finite non-zero number is

The integer ' n ' for which lim_(x->0)((cos x-1)(cos x-e^x))/(x^n) is a finite non-zero number, is a.1 b. 2 c. 3 d. 4

The natural number n,for which lim_(x rarr0x rarr0)((27^(x)-9^(x)-3^(x)+1)(cos x-e^(x)))/(x^(2n+1)) is a finite non zero number equal to

The integer ‘n’ for which the value of lim _( x to oo) (( 1- cos x) (e ^(x) - cos x) - (x ^(3))/( 2))/( x ^(n)) is a finite non zero number, is____.

The number of non-negative integral values of n for which lim_(x rarr0)((cos x-1)(cos x-e^(x)))/(x^(n))=0 is :