`T h ev a l u eofint_(sqrt(1n2))^(sqrt(1n3))(xsinx^2)/(sinx^2+sin(1n6-x^2))dxi s` `1/4 1n3/2` (b) `1/21n3/2` `1n3/2` (d) `1/61n3/2`

For all n in N, 1 + 1/(sqrt(2))+1/(sqrt(3))+1/(sqrt(4))++1/(sqrt(n))

The value of lim_(xtooo) {(1)/(3)+(2)/(21)+(3)/(91)+...+(n)/(n^4+n^2+1)} , is

If int1/(xsqrt(1-x^3))dx=alog|(sqrt(1-x^3)-1)/(sqrt(1-x^3)+1)|+b ,t h e n a is e q u a l 1/3 (b) 2/3 (c) -1/3 (d0 -2/3

lim_(n->oo)[1/sqrt(2n-1^2) +1/sqrt(4n-2^2)+1/sqrt(6n-3^2)+...+1/n]

Evaluate: ("lim")_(n rarr oo)(1/(sqrt(4n^2-1))+1/(sqrt(4n^2-2^2))++1/(sqrt(3n^2)))

The value of lim_(n -> oo)(1.n+2.(n-1)+3.(n-2)+...+n.1)/(1^2+2^2+...+n^2)

The area of the region whose boundaries are defined by the curves y= 2cosx , y= 3tanx and the y-axis is (a) 1+31n(2/(sqrt(3)))s qdotu n i t s (b) 1+3/2 1n3-31n2s qdotu n i t s (c) 1+3/2 1n3-1n2s qdotu n i t s (d) 1n3-1n2s qdotu n i t s

sum_(n=1)^oo sin^-1( (sqrt(n)-(sqrt(n-1)))/(sqrt((n)(n+1)) )= (A) pi/4 (B) pi/2 (C) - pi/3 (D) pi/3

underset(nrarroo)lim[(1)/(sqrtn)+(1)/(sqrt(2n))+(1)/(sqrt(3n))+...+(1)/(n)]

Prove that log_e ((n^2)/(n^2-1))=1/(n^2)+1/(2n^4)+1/(3n^6)+........oo