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

Using Lagranges mean value theorem,prove that (b-a)/(b)

Using Lagranges mean value theorem,prove that |cos a-cos b|<=|a-b|

Using Lagranges mean value theorem,show that sin(:x for x:)0.

Using Lagranges mean value theorem,prove that (b-a)sec^(2)a<(tan b-tan a)<(b-a)sec^(2)b where 0

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

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

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

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

Using Lagrange's mean value theorem prove that if b gt a gt 0 "then " (b-a)/(1+b^(2)) lt tan^(-1) b -tan^(-1) a lt (b-a)/(1+a^(2))

If a>b>0, with the aid of Lagranges mean value theorem,prove that nb^(n-1)(a-b) 1nb^(n-1)(a-b)>a^(n)-b^(n)>na^(n-1)(a-b),quad if 0