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, prove that (b-a)sec^2a lt (tanb-tana) lt (b-a)sec^2b , where 0ltaltbltpi/2

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

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

Using Lagranges mean value theorem, show that sinx 0.

Using Lagranges mean value theorem, find a point on the curve y=sqrt(x-2) defined on the interval [2,3], where the tangent is parallel to the chord joining the end points of the curve.

The value of c in Lagrange.s mean value theorem for the function f (x) = x ^(2) + x +1 , x in [0,4] is :

The value of c in Lagrange's mean value theorem for the function f(x) = |x| in the interval [-1, 1] is

The value of c in Lagrange 's mean value theorem for the function f(x)=x^(2)+x+1, x in[0,4]