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

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

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 the Lagrange's mean value theorem determine the values of x at which the tangent is parallel to the secant line at the end points of the given interval: f(x)=x^(3)-3x+2,x in[-2,2]

Using the Lagrange's mean value theorem determine the values of x at which the tangent is parallel to the secant line at the end points of the given interval: f(x)=(x-2)(x-7),x in[3,11]

Using mean value theorem prove that for , a gt 0, bgt 0, |e^(-a)-e^(-b)| lt| a-b|

Using mean value theorem prove that for, agt0,bgt0,|e^(-a)-e^(-b)|lt|a-b| .

Using intermediate value theorem, prove that there exists a number x such that x^(2005)+1/(1+sin^2x)=2005.

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

Find 'C' of Lagrange's mean value theorem for the function f(x) =x^(3)-5x^(2)-3x in [1, 3]