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Rolle's Theorem
Assume f(x) is a function which satisfies all of the following.
1. f(x) is continuous in the closed interval [a,b].
2. f(x) is differentiable in the open interval (a,b).
3. f(a) = f(b)
So, there is a number c as a < c < b and f′(c) = 0. Or, though f(x) has a critical point in (a,b).
Mean Value Theorem : Suppose f (x) is a function which satisfies both of the following. 1. f ( x )is continuous on the closed interval [a,b]. 2. f ( x ) is differentiable on
Find the value of x if 2x + 1, x 2 + x +1, 3 x 2 - 3 x +3 are consecutive terms of an AP. Ans: a 2 -a 1 = a 3 -a 2 ⇒ x 2 + x + 1-2 x - 1 = 3x 2 - 3x + 3- x
Series - Special Series In this part we are going to take a concise look at three special series. In fact, special may not be the correct term. All three have been named th
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If we "break up" the root into the total of two pieces clearly we get different answers. Simplified radical form: We will simplify radicals shortly so we have to next
cos^2a+sin^2a
whats nine plus 10
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(1) If the coefficient of friction between a box and the bed of a truck is m , What is the maximum acceleration with which the truck can climb a hill, making an angle q with the ho
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