If `lim_(n->oo)1/((sin^(-1)x)^("n")+1)=1` `,t h e n` find the value of x.

Let f(x)=lim_( n to oo)(cosx)/(1+(tan^(-1)x)^(n)) . Then the value of int_(o)^(oo)f(x)dx is equal to

lim_(n->oo)((n^2-n+1)/(n^2-n-1))^(n(n-1)) is

lim_(xto1)(x^(m)-1)/(x^(n)-1) is

If ("lim")_(xvecoo){(x^2+1)/(x+1)-(a x+b)}=0, then find the value of aa n dbdot

If lim(n->oo)(n*3^n)/(n(x-2)^n +n*3^(n+1)-3^n) = 1/3 then the range of x is (where n epsilon N )

If ("lim")_(xvec0)[1+x+(f(x))/x]^(1/x)=e^3, then find the value of 1n(("lim")_(xvec0)[1+(f(x))/x]^(1/x))i s____

If sin^(-1)x_1+sin^(-1)x_2++sin^(-1)x_nlt=-(npi)/2,n in N ,n=2m+1, mgeq1, then find the value of (x_1^1+x_3^3+x_5^5+...(m+1)t e r m s)/(x_2^2+x_4^ 4+x_6^ 6+.... mt e r m s)

If a_(1)=1 and a_(n)+1=(4+3a_(n))/(3+2a_(n)),nge1"and if" lim_(ntooo) a_(n)=a,"then find the value of a."

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

Compute lim_(xto1)(x^(m)-1)/(x^(n)-1) .