`lim_(u -> 1) (1 + u^(1/3)) / (1 + u^(1/5))`

lim_ (u rarr1) (1 + u ^ (1) / (3))) / (1 + u ^ ((1) / (5)))

The function u_(n) takes on the following values : u_(1) = ( 1)/( 4) , u_(2) = ( 1)/( 4) + ( 1)/( 10)"…....." u_(n) =(1)/( 3+1) + ( 1)/( 3^(2) + 1)+"…........." (1)/( 3^(n) + 1)"…........." Prove that underset( n rarr oo) ( "lim") u_(a) lt (1)/(2)

Let A""=(1 0 0 2 1 0 3 2 1) If u_1 and u_2 are column matrices such that A u_1=(1 0 0) and A u_2=(0 1 0) , then u_1+""u_2 is equal to (1) (-1 1 0) (2) (-1 1-1) (3) (-1-1 0) (4) (1-1-1)

For the sequence {u_(n)} if u_(1) = (1)/(4) and u_(n+1) = (u_(n))/(2+u_(n)) , find the value of (1)/(u_(50)) .

For the sequence {u_(n)} if u_(1) = (1)/(2) and u_(n+1) = (u_(n))/(1+2u_(n))(n ge 1) , find the value of u_(96) .

If y = (u -1)/(u + 1) and u = sqrt(x) , then (dy)/(dx) is