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

("lim")_(xvec0)(sinx^n)/((sinx)^m),(m

("lim")_(xvec0)(sinx^n)/((sinx)^m),(m

The value of the definite integral int_(sqrt2-1)^(sqrt(2)+1)(x^4+x^2+2)/((x^2+1)^2)dxe q u a l s___

lim_(n->oo)(n(2n+1)^2)/((n+2)(n^2+3n-1)) is equal to (a)0 (b) 2 (c) 4 (d) oo

Find the value of sum_(p=1)^n(sum_(m=p)^n^n C_m^m C_p)dot And hence, find the value of (lim)_(nvecoo)1/(3^n)sum_(p=1)^n(sum_(m=p)^n^n C_m^m C_p)dot

Evaluate: ("lim")_(nvecoo)[1/(n^2)sec^2 1/(n^2)+2//n^2sec^2 4/(n^2)++1/nsec^2 1]

Find the number of integers lying in the interval (0,4) where the function f(x)=(lim)_(nvecoo)(cos(pix)/2)^(2n) is discontinuous

If a_1=1a n da_(n+1)=(4+3a_n)/(3+2a_n),ngeq1,a n dif("lim")_(nvecoo)a_n=a , then find the value of adot

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")_(nvecoo)"{"(n/(n+1))^(alpha)+sin(1/n)]^n (when alpha in Q ) is equal to (a) e^(-alpha) (b) -alpha (c) e^(1-alpha) (d) e^(1+alpha)