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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).
what is the consective sum for 2+3
The bowling alley suggests selecting a ball that is 1/7 of the bowlers weight. If the bowler weighs 84 pounds, how much should the bowling ball weigh?
Solving Trig Equations with Calculators, Part II : Since this document is also being prepared for viewing on the web we split this section into two parts to keep the size of the
R is called as a transitive relation if (a, b) € R, (b, c) € R → (a, c) € R In other terms if a belongs to b, b belongs to c, then a belongs to c. Transitivity be uns
Fundamental Theorem of Calculus, Part II Assume f ( x ) is a continuous function on [a,b] and also assume that F ( x ) is any anti- derivative for f ( x ) . Then,
Solve by factorization X 2 +(a/a+b + a+b/a)x+1 = 0 X 2 +(a/a+b + a+b/a)x+1 => X 2 +(a/a+b x a+b/ax + a/a+b .a+b/a) => X[x+a/a+b] +a+b/a[a+a*a+b]= 0 => X= -a
1. Use mathematical induction to prove whenever n is a positive integer. 2. Use loop invariant to prove that the program for computing the sum of 1,...,n is correct.
The mode - It is one of the measures of central tendency. The mode is defined as a value in a frequency distribution that has the highest frequency. Occasionally a single valu
Melisa and Jennifer threw a fiftieth birthday party for their father at a local restaurant. While the bill came, Melisa added a 15% tip of $42. Jennifer said in which the service w
Write down the system of differential equations for mass system and the spring above. Solution To assist us out let's first take a rapid look at a situation wherein both of
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