If `xgt0` prove that `x+ 1/x ge2`

If x,y,z gt 0 and x + y + z = 1, the prove that (2x)/(1 - x) + (2y)/(1 - y) + (2z)/(1 - z) ge 3 .

Use principle of mathematical induction, to prove that (1 + x) ^(n) gt 1 + nx , " for " n ge 2 and x gt = -1, (ne 0 )

For the given statement identify the necessary and sufficent conditions r : If x is real number such that xgt0 " then " x+1/xge2

If xgt0 then (x-1)/(x+1)+(1)/(2)(x^(2)-1)/((x+1)^(2))+(1)/(3)(x^(3)-1)/((x+1)^(3))+....=

Solve the inequation: (x+1)/(x-7) ge2

For xgt1 , show that: 2log_10x-log_x 0.01ge4

Prove that e^(x) ge 1 +x and hence e^(x) +sqrt(1+e^(2x))ge(1+x)+sqrt(2+2x+x^(2)) forall x in R

If (-3)/(x)+4le-11 and xgt0 , what ist he greatest possible value for x?

A curve passes through the point (1,(pi)/(6)). Let the slope of the curve at each point (x,y) be (y)/(x)+sec((y)/(x)),xgt0. Then, the equation of the curve is