`("lim")_(xtooo)(a n-(1+n^2)/(1+n))=b ,` where `a` is a finite number, then(a) `a=1` (b) `a=0` (c) `b=1` (d) `b=-1`

If ("lim")_(xrarr0)({(a-n)n x-tanx}sinn x)/(x^2)=0, where n is nonzero real number, the a is 0 (b) (n+1)/n (c) n (d) n+1/n

("lim")_(xtooo)1/(1+nsin^2n x)is equal (a)-1 (b) 0 (c) 1 (d) oo

("lim")_(x->oo){(x^3+1)/(x^2+1)-(a x+b)}=2,t h e n (a) a=1,b=1 (b) a=1,b=2 (c) a=1,b=-2 (d) none of these

Evaluate lim_(xtooo) (1+(1)/(a+bx))^(c+dx) , where a, b, c, and d are positive.

If lim_(x->0)(x^n-sinx^n)/(x-sin^n x) is non-zero finite, then n must be equal to 4 (b) 1 (c) 2 (d) 3

("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)

If y=(1+t a n A)(1-t a n B), where A-B=pi/4, then (y+1)^(y+1) is equal to 9 (b) 4 (c) 27 (d) 81

If ("lim")_(xto1^-)(2-x+a[x-1]+b[1+x]) exists, then aa n db can take the values of (where [.] denotes the greatest integer function). (a) a=1/3,b=1 (b) a=1, b=-1 (c) a=9, b=-9 (d) a=2, b=2/3

For a in R (the set of all real numbers), a!=-1), (lim)_(n->oo)((1^a+2^a++n^a)/((n+1)^(a-1)[(n a+1)+(n a+2)+......(n a+n)])=1/(60.) Then a= (a) 5 (b) 7 (c) (-15)/2 (d) (-17)/2

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