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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).
A solution to a differential equation at an interval α Illustration 1: Show that y(x) = x -3/2 is a solution to 4x 2 y′′ + 12xy′ + 3 y = 0 for x > 0. Solution : We'll
Assumptions and Application of T Distribution Assumptions of t distribution 1. The sample observations are random 2. Samples are drawn from general distribution 3.
rajan bought an armchair for rs.2200 and sold it for rs.2420.find his profit per cent.
Correlation and Regression CORRELATION is an important statistical concept which refers to association or interrelationship among variables. The reasons of studying correla
Q. How to Subtract fractions involving negative numbers? Ans. This is the same as adding them, but just remember the rule that two negatives on the same fraction cancel ou
Dot Product- Vector The other topic for discussion is that of the dot product. Let us jump right into the definition of dot product. There is given that the two vectors a
ALGORITHM FOR DIVISION : If you ask a 10 or 1 1-year-old child to solve, say, 81 + 9, the chances are that she will correctly do it. But if you ask her to solve, say 72 + 3, t
Example of line - Common Polar Coordinate Graphs Example: Graph θ = 3Π, r cos θ = 4 and r sin θ = -3 on similar axis system. Solution There actually isn't too much to
Solve 8 cos 2 (1 - x ) + 13 cos(1 - x )- 5 = 0 . Solution Now, as specified prior to starting the instance this quadratic does not factor. Though, that doesn't mean all i
STATISTICS AND PROBABILITY : Statistics are the only tools by which an opening can be cut through the formidable thicket of difficulties that bars the path of
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