`(lim)_(nvecoo)n/(2^n)int_0^2x^n dxe q u a l s___`

The value of (lim)_(nvecoo)((a+1+b n)/a)^n ; a ,b >0,a n dn in N is equal to:

S1: lim_(n->oo) (2^n + (-2)^n)/2^n does not exist S2: lim_(n->oo) (3^n + (-3)^n)/4^n does not exist

If I_n=int_0^(sqrt(3))(dx)/(1+x^n),(n=1,2,3. .), then find the value of ("lim")_(nvecoo)I_ndot (a)0 (b) 1 (c) 2 (d) 1/2

f(x)>0AAx in Ra n di sbou n d e ddotIf (lim)_(nvecoo)[int_0^a(f(x)dx)/(f(x)+f(a-x))+a^2+aint_a^(2a)(f(x)dx)/(f(x)+f(3a-x))+int_(2a)^(3a)(f(x)dx)/(f(x)+f(5a-x))++a^(n-1)int_((n-1)a)^(n a)(f(x)dx)/(f(x)+f[2n-1)a-x])]=7//5 (where a<1), then a is equal to 2/7 (b) 1/7 (c) (14)/(19) (d) 9/(14)

lim_(n rarr0)(sin2n)/(2n^(2)+n)

l_(n)=int_(0)^(pi//4)tan^(n)xdx , then lim_(nto oo)n[l_(n)+l_(n-2)] equals

Let f(x)=("lim")_(nvecoo){("lim")_(nvecoo)cos^(2m)(n !pix)}, where x in Rdot Then prove that f(x)={1,ifxi sr a t ion a l0,ifxi si r r a t ion a l

If m, n in N , then l_(m n) = int_(0)^(1) x^(m) (1-x)^(n) dx is equal to

(2) lim_(n rarr0) (n!sin x)/(n)