If `lim_(x->1)((x^n-1)/(n(x-1)))^(1/(x-1))=e^p` , then p is equal to

Let p=lim_(x->0^+)(1+tan^2 sqrt(x))^(1/(2x)) then log p is equal to

lim_(x->oo)(1-x+x.e^(1/n))^n

If lim_(x->0)[1+x+(f(x))/x]^(1/x)=e^3, then find the value of 1n(lim_(x->0)[1+(f(x))/x]^(1/x))i s____

lim_(x->oo)n^2(x^(1/n)-x^(1/((n+1)))),x >0 , is equal to (a)0 (b) e^x (c) (log)_e x (d) none of these

lim_(xrarr1)(x^(m)-1)/(x^(n)-1) is equal to

lim_(xrarr1)(x^(m)-1)/(x^(n)-1) is equal to

lim_(xto1) (nx^(n-1)-(n+1)x^(n)+1)/((e^(x)-e)sinpix) , where n=100 ,is equal to

If lim_(x rarr(oo) (1+(1)/(x(x+2)))^(x^(2))(1+(1)/(x(x+4)))^(-x^(2)) is equal to e^(n) then n is equal to

lim_(x rarr oo)n^(2)(x^((1)/(n))-x^((1)/((n+1)))),x>0, is equal to (a)0(b)e^(x)(c)(log)_(e)x(d) none of these