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

Using Lagrange's mean value theorem prove that, e^(x) gt 1 +x

Using Largrange's mean value theorem, prove that, b^(n)-a^(n) gt n a^(n-1)(b-a)" when " b gt a .

Using Lagrange's mean value theorem prove that, log (1+x) lt x ("when " x gt 0)

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) .

State Lagrange's mean value theorem.

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

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, (b-a)/(b) lt "log"(b)/(a) lt (b-a)/(a) , where 0 lt a lt b .

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