`(x-1)/(x+1)ltx`

prove that (x)/(1+x) lt log (1+x)ltx , for all xgt 0

prove that (x)/(1+x) lt log (1+x)ltx , for all xgt 0

(4x)/3-9/4ltx+3/4; (7x-1)/3-(7x+2)/6>x

A bag contains 30 tickets numbered from 1 to 30 . Five tickets are drawn at random and arranged in ascending order . Find the probability that the third number is 20. (ii) a bag contains 50 tickets numbered 1,2,3 ……, 50 of which five are drawn at random and arranged in ascending order of magnitude (x_(1)ltx_(2)ltx_(3)ltx_(4)ltx_(5)) . What is the probability that x_(3)=30 .?

If 0ltx

If 0ltx

A bag contains 50 tickets marked with numbers 1,2,…………….50. Five tickets are selected at random from the bag and arranged in ascending order x_(1)ltx_(2)ltx_(3)ltx_(4)ltx_(5) . Find the probability that x_(3)=30 .

If xsqrt(1+y)+ysqrt(1+x)=0 for -1ltx,ylt1 then prove that (dy)/(dx)=(-1)/((x+1)^(2))

Diseuss the continuity of the function : {:(f(x)=(sin 2x)/(sqrt(1-cos2x)),",for"0ltx le(pi)/(2)),(=(cosx)/(pi-2x),",for" (pi)/(2)ltx ltpi):}}at x=(pi)/(2)*