The integer `n` for which `("lim")_(xvec0)((cosx-1)(cosx-ehatx)/(x^n)` is finite nonzero number is ________

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

Evaluate ("lim")_(xvec0) (sinx-2)/(cosx-1)

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

Evaluate: ("lim")_(xvec0)(cot2x-cos e c2x)/x

("lim")_(xvec0)(5sinx-7sin2x+3sin3x)/(x^2sinx)

Evaluate: ("lim")_(xvec0)(1-cos2x)/(x^2)

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

Evaluate: ("lim")_(xvec0)(1-cosm x)/(1-cosn x)

Evaluate: ("lim")_(xvec0)(1+x)^(os e cx c)

Evaluate: ("lim")_(xvec0)(sin^(-1)x-tan^(-1)x)/(x^3)