`E={x : x=n/(n+1), n in N}`

Write each of the following sets in Roster form and write the cardinal number of each . E = {x: x =2n- 1 , n in N and n lt 6.}

Show that int x ^(n) . e ^(-x) dx= -x^(n) e ^(-x) +n int x ^(n-1) . e ^(-x) dx

Let f _(1)(x) =e ^(x) and f _(n+1) (x) =e ^(f _(n)(x))) for any n ge 1, n in N. Then for any fixed n, the vlaue of (d)/(dx) f )(n)(x) equals:

Let f _(1)(x) =e ^(x) and f _(n+1) (x) =e ^(f _(n)(x))) for any n ge 1, n in N. Then for any fixed n, the vlaue of (d)/(dx) f )(n)(x) equals:

If n(ne 1) in N and I_(n) = int e^(x)/x^(n) dx then I_(n)+ e^(x)/((n-1)x^(n-1))

lim_(x->oo)(e^x((2^(x^n))^(1/(e^(x)))-(3^(x^n))^(1/(e^(x)))))/(x^n), n in N, is equal to

The value of ""(n)C_(1). X(1 - x )^(n-1) + 2 . ""^(n)C_(2) x^(2) (1 - x)^(n-2) + 3. ""^(n)C_(3) x^(3) (1 - x)^(n-3) + ….+ n ""^(n)C_(n) x^(n) , n in N is

The value of ""(n)C_(1). X(1 - x )^(n-1) + 2 . ""^(n)C_(2) x^(2) (1 - x)^(n-2) + 3. ""^(n)C_(3) x^(3) (1 - x)^(n-3) + ….+ n ""^(n)C_(n) x^(n) , n in N is

If = int_(0)^(1) x^(n)e^(-x)dx "for" n in N "then" I_(n)-nI_(n-1)=