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

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

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

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

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

If f(x) = (x-1)(x-2) and a = 0, b = 4 , find 'c' using Lagrange's mean value theorem.

Find the value of c in Lagrange's mean value theorem for the function f (x) = log _(e) x on [1,2].

The value of c in Lagrange's mean value theorem for the function f(x)=log_ex in the interval [1,3] is

Varify Lagrange's mean value theorem for the function f(x)=x+(1)/(x), x in [1, 3]

Verify Lagrange's mean value theorem for the function f(x) = 2x^(2) -10 x + 29 in the interval [2.7]