[li_(x rarr alpha)((a^(1/x)+b^(1/x)+c^(1/x))/(3))=],[" real and non zero) "]quad (" where "a,b,c" are "

lim_(x rarr oo)((a^(1/x)+b^(1/x)+c^(1/x))/3)^x , where a, b, c are real and non zero =

lim_(x rarr oo)((a^((1)/(x))+b^((1)/(x))+c^((1)/(x)))/(3))^(x)

li_(x rarr0)(sqrt(1+x)-1)/((1+x)^((1)/(3))-1)

Lt_(x to oo) ((a^((1)/(x))+b^((1)/(x))+c^((1)/(x)))/(3))^(x) when a,b,c are non zero positive real numbers)=

If lim_(x rarr oo)((a^(1/x)+b)/(c))^(x)=d( non zero finite ) then (b+1)log_(a)d is

underset(x to oo )"Lt" [(a^(1//x)+b^(1//x)+c^(1//x))/(3)]^(x), where a,b,c are real and nonzero=

lim_(x->0)(1+(asinb x)/(cosx))^(1/x), where a,b are non zero constants is equal to :

lim_(x->0)(1+(asinb x)/(cosx))^(1/x), where a,b are non zero constants is equal to :

lim_(x rarr0)(1-cos(1-cos x))/(x^(n))=l a finite non- zero value then n=(a)1(b)2(c)3(d)4