" (vii) "p(u)=4u^(2)+1;u=(1)/(4)

if a+ib=((u+i)^(2))/(2u-i) then prove that a^(2)+b^(2)=((u^(2)+1)^(2))/(4u^(2)+1)

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)

the abscissae of any two points on the parabola y^(2)=4ax are in the ratio u:1. prove that the locus of the point of intersection of tangents at these points is y^(2)=(u^((1)/(4))+u^(-((1)/(4))))^(2)ax

The function u_(n) attains the values u_(1) = (1)/( 2) , u_(2) = ( 1)/( 2) +( 1)/( 2.4) + ( 1)/( 2.4.6) u_(n) = ( 1)/( 2) + ( 1)/( 2.4) + "...." ( 1) /( 2.4 "...." ( 2n )) ,"............" Prove that underset( n rarr oo) ( "lim") u_(n) lt 2

If y=(1)/(4)u^(4),u=(2)/(3)x^(3)+5 , then (dy)/(dx)=

If P(A)= (1)/(4), P(B)= (1)/(3) and P(A U B)= (1)/(2) , prove that A and B are independent events

If quad tan((1)/(2)(cos^(-1))(1-u^(2))/(1+u^(2))+(1)/(2)(sin^(-1))(2u)/(1+u^(2))) and x=(2u)/(1-u^(2)) then (dy)/(dx)