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

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

Using Rolles theorem, prove that there is at least one root in (45^(1/(100)),46) of the equation. P(x)=51 x^(101)-2323(x)^(100)-45 x+1035=0.

int(cosec^2x-2005)/cos^[2005]x.dx

The value of c in Lagrange's mean value theorem for the function f(x) = x^(2) + 2x -1 in (0, 1) is

Verify mean value theorem for the function f(x) = x^(3) - 5x^(2) _ 2x in [1, 3]

The number given by the Mean value theorem for the function 1/x,x in[1,9] is

Find the values in the interval (1,2) of the mean value theorem satisfied by the function f(x)=x-x^(2) "for" 1 le x le 2 .

Verify Lagrange's mean value theorem for f(x) = (1)/(x) " in " [1, 2]

Show that the value in the conclusion of the mean value theorem for f(x)=1/x on a closed interval of positive numbers [a, b] is sqrt(ab) .