Using Lagranges mean value theorem, prove that `(b-a)/bltlog(b/a)lt(b-a)/a,`where `0ltaltbdot`

Using Lagranges mean value theorem, prove that (b-a)/b < log(b/a) < (b-a)/a ,w h e r e 0 < a < bdot

Using Lagranges mean value theorem, show that sinx 0.

Using Lagranges mean value theorem, prove that |cosa-cosb|<|a-b|dot

Using Lagranges mean value theorem, prove that |cosa-cosb|<=|a-b|dot

Using Lagranges mean value theorem, prove that (b-a)sec^2a lt (tanb-tana) lt (b-a)sec^2b , where 0ltaltbltpi/2

Using lagrange's mean value theorem, show that (beta-alpha)/(1+beta^2) alpha > 0.

In [0, 1] Lagrange's mean value theorem is not applicable to

Using mean value theorem, prove that tanx > x for all x(0,pi/2)dot

If from Largrange's mean value theorem, we have f'(x(1))=(f'(b)-f(a))/(b-a) then,

In [0,1] , lagrange mean value theorem is NOT applicable to