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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).
Complex Numbers In the radicals section we noted that we won't get a real number out of a square root of a negative number. For example √-9 isn't a real number as there is no
Proof of the Properties of vector arithmetic Proof of a(v → + w → ) = av → + aw → We will begin with the two vectors, v → = (v 1 , v 2 ,..., v n )and w? = w
Laws of Set Algebra From the given Venn diagram where T is the universal set and A its subset that we can deduce a number of laws as: i. A υ Ø = A ii. A υ T = T
project assignment of page no.19 question no.2
Which of the subsequent numbers is equivalent to 12.087? Zeros can be added to the end (right) of the decimal portion of a number without changing the value of the number; 12.
Two angles are complementary. The larger angle is 15° more than twice the smaller. Find out the measure of the smaller angle. Let x = the number of degrees in the smaller angle
Higher Order Derivatives : Let's begin this section with the given function. f ( x ) = 5x 3 - 3x 2 + 10 x - 5 By this point we have to be a
If the difference among the squares of two consecutive integers is 15 find out the larger integer. Let x = the lesser integer and let x + 1 = the greater integer. The sentence,
6987+746-212*7665
1. A psychologist developed a test designed to help predict whether production-line workers in a large industry will perform satisfactorily. A test was administered to all new empl
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