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The Mean Value Theorem : In this section we will discuss the Mean Value Theorem.
Before we going through the Mean Value Theorem we have to cover the following theorem.
Rolle's Theorem : Assume f ( x ) is a function which satisfies all of the following.
1. f ( x ) is continuous on the closed interval [a,b].
2. f ( x ) is differentiable on the open interval (a,b).
3. f ( a ) =f (b )
Then there is a number c such that a < c < b and f ′ (c ) = 0 . Or, in other terms f ( x ) contain a critical point in (a,b).
Characteristics of Time Series Time series has the given characteristics. a) A long term trend (T) -tendency of the whole series to fall and rise. b) Seasonal variati
Which of the subsequent decimals is the greatest number? If you add zeros to the end of every of the numbers so that each number has 5 places after the decimal point, it is sim
Sums and Differences of Cubes (and other odd powers)? You can factor a sum or difference of cubes using the formulas a 3 - b 3 = (a - b )(a 2 + ab + b 2 ) and a 3 + b 3 =
(2a+8b)
In the earlier section we modeled a population depends on the assumption that the growth rate would be a constant. Though, in reality it doesn't make much sense. Obviously a popula
In Figure, what are the angles of depression from the observing positions O 1 and O 2 of the object at A?
Curvature - Three Dimensional Space In this part we want to briefly discuss the curvature of a smooth curve (remind that for a smooth curve we require → r′ (t) is continuou
Each of the series 3+5+7+..... and 4+7+10.......... is continued to 100 terms find how many terms are identical. Ans) 48 terms would be common to both the series... first take co
Saddle Point This point in a pay off matrix is one which is the largest value in its column and the smallest value in its row. This is also termed as equilibrium point in the t
how to simplify fractions
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