Use the mean value theorem to prove `e^(x)ge1+xAA xinR`

Use the mean value theorem to prove e^xgeq1+xAAx in R

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

Using mean value theorem, prove that there is a point on the curve y = 2x^(2) - 5x+3 between the points A(1,0) and B(2,1) , where tangent is parallel to the chord AB . Also, find that point.

Using mean value theorem, prove that there is a point on the curve y = 2x^(2) - 5x+3 between the points A(1,0) and B,(2,1) , where tangent is parallel to the chord AB . Also, find that point.

Using mean value theorem, prove that tanx > x for all x(0,pi/2)dot

Using Lagranges mean value theorem, prove that (b-a)/b < log(b/a) < (b-a)/a ,w h e r e 0 < a < bdot

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

Verify Lagrange's mean value theorem for f(x)= x-2 sin x "in " [-pi, pi]

Using Lagranges mean value theorem, prove that (b-a)sec^2a lt (tanb-tana) lt (b-a)sec^2b , where 0ltaltbltpi/2

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