If `x_1=3` and `x_(n+1)=sqrt(2+x_n),ngeq1,t h e n""("lim")_(xrarroo)x_n` is (a) `-1` (b) `2` (c) `sqrt(5)` (d) 3

If G(x)=-sqrt(25-x^2),t h e n lim_(x->1)(G(x)-G(1))/(x-1)i s (a) 1/(24) (b) 1/5 (c) -sqrt(24) (d) none of these

If a_n and b_n are positive integers and a_n+sqrt(2)b_n=(2+sqrt(2))^n ,t h e n(lim)_(x->oo)((a_n)/(b_n))= a. 2 b. sqrt(2) c. e^(sqrt(2)) d. e^2

For x in R , lim_(xrarroo)((x-3)/(x+2))^x is equal to (a) e (b) e^(-1) (c) e^(-5) (d) e^5

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

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

If y=tan^(-1)sqrt((x+1)/(x-1)),t h e n(dy)/(dx)i s (-1)/(2|x|sqrt(x^2-1)) (b) (-1)/(2xsqrt(x^2-1)) 1/(2xsqrt(x^2-1)) (d) none of these

If f^(prime)(x)=sqrt(2x^2-1)a n dy=f(x^2),t h e n(dy)/(dx)a tx=1 is 2 (b) 1 (c) -2 (d) none of these

Let I_(n)=int_(0)^(1)x^(n)sqrt(1-x^(2))dx. Then lim_(nrarroo)(I_(n))/(I_(n-2))=

If y=sqrt(logx+sqrt(logx+sqrt(logx+oo))),t h e n(dy)/(dx)i s (a) x/(2y-1) (b) x/(2y+1) (c) 1/(x(2y-1)) (d) 1/(x(1-2y))

If y=tan^(-1)((2^x)/(1+2^(2x+1))),t h e n(dy)/(dx)a tx=0 is (a)1 (b) 2 (c) 1n 2 (d) none of these