tathagata

Tell me a number which when divided, multiplied, added & subtracted by a x number gives a same number, for example when 2 is divided with 2 it gives 1 & multiplied with 2 give 4 . Therefore the number is not matching.

Let consider: Lim x -> 0 {f(x)}^g(x), where as x -> 0 ,f(x) -> 1,and g(x) ->infinity lim x->0 [f(x)]^g(x)=lim x->0[1+f(x)-1]^{{g(x)(f(x)-1)}/(f(x)-1)} = e^lim x ->0{g(x)(f(x)-1)} here ,we consider only the part; lim x->0 (e^x)^(1/x) f(x)=e^x and g(x)=1/x so limit becomes : e^[lim x->0 ((e^x-1)/x)=e^1=e :as (e^x-1)/x=1