[" Let "lim_(x rarr oo)x ell n(e(1+(1)/(x))^(1-1))" equal "(m)/(n)" where "m" and "n" are relatively prime positive integer.Find "],[(m+n)" ."]

Let lim_(x rarr oo)x ln(e(1+(1)/(x))^(1-x)) equal (m)/(n) where m and n are relatively prime positive integ Find (m+n).

lim_(x rarr oo)(1-x+x*e^((1)/(n)))^(n)

Let lim _( x to oo) n ^((1)/(2 )(1+(1 )/(n))). (1 ^(1) . 2 ^(2) . 3 ^(3)....n ^(n ))^((1)/(n ^(2)))=e^((-p)/(q)) where p and q are relative prime positive integers. Find the value of |p+q|.

let f(x)=lim_(n rarr oo)(x^(2n)-1)/(x^(2n)+1)

Given that sum_(k=1)^(35)sin5k^(@)=tan((m)/(n))^(@), where m and n are relatively prime positive integers that satisfy ((m)/(n))^(@)<90^(@), then m+n is equal to

int_(0)^(1)x^((m-1))(1-x)^((n-1))dx is equal to where m,n in N

FInd lim_ (n rarr oo) n ^ (n) (n + 1) ^ (m-1) -: n ^ (4)

Given that sum_(k=1)^35 sin5k^@ = tan(m/n)^@ , where m and n are relatively prime positive integers that satisfy (m/n)^@<90^@ , then m + n is equal to