Все публикации

0:04:56

If function f(x) and g(x) are cont. in [a,b] and diff. in (a,b), show that there will be at least

0:03:04

Prove that f(1)+f(3) \greater 2f(2),where f'(x) is strictly increasing function.

0:04:24

Let f(x) be a diff. function for all x€R,such that f'(x) \ge 1for x€R.If f(0) =2,f(3)=6 then f(2)

0:05:20

If f(x) is twice diff. function such that f(1)=1,f(2)=2,f(3)=3,then prove that f'(c)=0 for least one

0:04:06

If f(x) is cont. in [0,2] and diff in (0,2) and f(0)=2,f(2)=8,f'(x)\leq 3 for x€[0,2].Find f(1).

0:03:23

Using LMVT to prove that |cos a - cos b| \leq |a-b|.

0:02:54

Use LMVT to prove that tanx \greater x for x€(0,pi/2).

0:03:04

If a \less b,show that a real number 'c' can be found in (a,b) such that 3c^2 = a^2 +ab +b^2.

0:03:34

Find a point on the curve f(x)=sqrt(x-2) in [2, 3] where the tangent is parallel to the chord join

0:15:26

Lagrange's Mean Value Theorem [LMVT]

0:07:45

For a polynomial g(x) with real coefficient,let mg denote the number of distinct real roots of g(x)

0:05:20

If p(x)=51x^101 - 2323x^100 - 45x + 1035,using Rolle's theorem,prove that atleast one root of p(x)

0:05:57

Let f(x) and g(x) be differentiable function such that f'(x).g(x) \neq f(x).g'(x) for any real x.

0:08:06

Let P(x) be a polynomial with real coefficients. Let a,b €R, a less b be the two consecutive roots

0:03:18

Let n€N.If the value of c prescribed in Rolle's theorem for the function f(x) =2x(x-3)^n on [0, 3]

0:03:24

Verify Rolle's theorem for:f(x)=|x|^3 in [-1 1].

0:02:06

Verify Rolle's theorem for:f(x) =1-x^2/3 in [-1 1]

0:03:54

Verify Rolle's theorem for: f(x) =sinx/e^x in [0,π]

0:05:49

Verify Rolle's theorem for :f(x)=x(x+3)e^-x/2 in [-3,0].

0:09:35

Rolle's Theorem

0:03:59

Find the smallest positive constant A such lnx \le Ax^2 for all x \ge 0

0:10:25

Prove that 2/(2x+1) \le ln(1+1/x) \le 1/x for x \ge 0

0:05:59

Prove that tanx/x greater than x/sinx for x €(0,pi/2).

0:02:26

Prove that :(4cos^2 9°- 3)(4cos^2 27°- 3)=tan9°