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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).
Theorem If {a n } is bounded and monotonic then { a n } is convergent. Be cautious to not misuse this theorem. It does not state that if a sequence is not bounded and/or
2/6
simplify mn+mp+nq+pq /n+p
how to multply
01010011 01100101 01101101 01110000 01100101 01110010 00100000 01000110 01101001 00100001
Proof of Sum/Difference of Two Functions : (f(x) + g(x))′ = f ′(x) + g ′(x) It is easy adequate to prove by using the definition of the derivative. We will start wi
The sum of two consecutive even integers is the number 126. What are the integers? Two consecutive even integers are numbers in sequence, such as 4 and 6 or -30 and -32, that a
2(sin 6 ?+cos 6 ?) - 3(sin 4 ?+cos 4 ?)+1 = 0 Ans: (Sin 2 ?)3 + (Cos 2 ?)3-3 (Sin 4 ?+(Cos 4 ?)+1=0 Consider (Sin 2 ?)3 +(Cos 2 ?)3 ⇒(Sin 2 ?+Cos 2 ?)3-3 Sin 2 ?Co
Can two lines contain a given point
Place ten pebbles (or any other such objects) in front of a child who can recite number names upto ten in the correct sequence. Ask him/her to count them aloud while touching the p
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