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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).
application
Find the 20 th term from the end of the AP 3, 8, 13........253. Ans: 3, 8, 13 .............. 253 Last term = 253 a20 from end = l - (n-1)d 253 - ( 20-1) 5 253
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Let 0 ! V1 ! ! Vk ! 0 be a long exact sequence of vector spaces with linear maps. Show that P (??1)i dim Vi = 0.
A series is said to be in Arithmetic Progression (A.P.) if the consecutive numbers in the series differs by a constant value. This constant value is referre
Josephine is constructing an open box by cutting the squares off the corners of a sheet of paper sized 20cm by 16cm. She is considering options of 3cm, 4cm and 5cm squares in order
Statistical inference This is the process of drawing conclusions about attributes of a population based upon information contained in a sample or taken from the population.
what is the value of zero to the power raised to zero?
rules for intergers
Under this section we will be looking at the previous case for the constant coefficient and linear and homogeneous second order differential equations. In this case we need soluti
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