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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).
example with solution of quadratic polynomial
Given two functions f(x) and g(x) which are differentiable on some interval I (1) If W (f,g) (x 0 ) ≠ 0 for some x 0 in I, so f(x) and g(x) are linearly independent on the int
#questio Study A Study B Study C x2 = 1.683 F = 7.357 r = .83 df = 4
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Mr. Hoper is in charge of investments for the golden horizon company. He estimates from past price fluctuations in the gold market that the probabilities of price changes on a give
If the roots of the equation (a-b) x 2 + (b-c) x+ (c - a)= 0 are equal. Prove that 2a=b+c. Ans: (a-b) x 2 + (b-c) x+ (c - a) = 0 T.P 2a = b + c B 2 - 4AC = 0
application of radious of curvatur
what is the value of integration limit n-> infinity [n!/n to the power n]to the power 1/n Solution) limit n-->inf. [1 + (n!-n^n)/n^n]^1/n = e^ limit n-->inf. {(n!-n^n)
Prove that Prim's algorithm produces a minimum spanning tree of a connected weighted graph. Ans: Suppose G be a connected, weighted graph. At each iteration of Prim's algorithm
4.2^2x+1-9.2^x+1=0
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