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, e^(x) gt 1 +x

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))

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

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 (b-a)/bltlog(b/a)lt(b-a)/a ,where 0ltaltb

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 (b-a)/bltlog(b/a)lt(b-a)/a="" a, where 0ltaltbdot

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 .

The value of c in Lagrange's mean value theorem for the function f(x) = log (sin x ) in the interval [(pi)/(6), (5pi)/(6)] is :