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Fermat's Theorem : If f ( x ) contain a relative extrema at x = c & f ′ (c ) exists then x = c is a critical point of f ( x ) . Actually, it will be a critical point such that f
Both need to be a full page, detailed proof. Not just a few lines of proof. (1) “Every convergent sequence contains either an increasing, or a decreasing subsequence (or possibly
The Mean Value Theorem for Integrals If f(x) is a continuous function on [a,b] then here is a number c in [a,b] thus, a ∫ b f(x) dx = f(c)(b -a) Proof Let's begin
Continuous Random Variable In the probability distribution the sum of all the probabilities was 1. Consider the variable X denoting "Volume poured into a 100cc cup from coff
To find the distance to nearby stars, the method of parallax is used. The idea is to find a triangle with the star at one vertex and with a base as large as possible. To do this, t
Natural exponential function : There is a extremely important exponential function which arises naturally in several places. This function is called as the natural exponential fun
If three times the larger of the two numbers is divided by the smaller, then the quotient is 4 and remainder is 5. If 6 times the smaller is divided by the larger, the quotient is
25 algebraic equations that equal 36
How the property AM>or = GM used to get minimum value of the function......e,g for what condition of a and b does minimum value of a tan^2 x + b cot^2 x equals maximum value of a
compare: 643,251: 633,512: 633,893. The answer is 633,512.
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