Using Lagrange's mean value theorem show that,
`(b-a)/(b) lt "log"(b)/(a) lt (b-a)/(a)`, where ` 0 lt a lt b`.

Using Largrange's mean value theorem, prove that, tan^(-1)x lt x

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

Using Lagrange's mean value theorem prove that, (b-a)sec^(2)a lt tan b-tan a lt (b-a)sec^(2)b when 0 lt a lt b lt (pi)/(2) .

Using Lagrange's mean value theorem prove that, log (1+x) lt x ("when " x gt 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

Lagrange's mean value theorem is , f(b)-f(a)=(b-a)f'(c ), a lt c lt b if f(x)=Ax^(2)+Bx+c" in " a le x le b , find c.

Lagrange's mean value theorem is , f(b)-f(a)=(b-a)f'(c ), a lt c lt b if f(x)=sqrt(x) and a=4, b=9, find c.

Applying Lagrange's mean value theorem for a suitable function f(x) in [0, h], we have f(h)=f(0)+hf'(thetah),0 lt theta lt1 . Then for f(x)=cosx , the value of underset(h to0+)lim theta is-

If x gt 0 , show that, log (1+x) lt x