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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).
Differentiate following. Solution : It requires the product rule & each derivative in the product rule will need a chain rule application as well. T ′ ( x ) =1/1+(2x) 2
Question: Find all third order partial derivatives for the function F(x,y)= log xy+ e (x+y) -x/y.
3/5 of the soda purchased at the football game was cola. What percentage of the soda purchased was cola? Change the fraction to a decimal through dividing the numerator through
Measures of Central Tendency Measures of Central Tendency are statistical values which tend to happen at the centre of any well ordered set of data. When these measures happen
As noted, Euler's method is little used in practice, as there are much better ways of solving initial value problems. By better, we mean, "able to achieve a result of the same prec
If a school has lockers with 50 numbers on each combination lock, how many possible combinations using three numbers are there.
A polynomial satisfies the following relation f(x).f(1/x)= f(x)+f(1/x). f(2) = 33. fIND f(3) Ans) The required polynomial is x^5 +1. This polynomial satisfies the condition state
Any point on parabola, (k 2 ,k) Perpendicular distance formula: D=(k-k 2 -1)/2 1/2 Differentiating and putting =0 1-2k=0 k=1/2 Therefore the point is (1/4, 1/2) D=3/(32 1/2
Eliment t from following equations v=u+at s=ut+1/2at^2
Question 1. Use cylindrical coordinates to nd the mass of the solid of density e z which lies in the closed region Question 2. The density of a hemisphere of radius a (y
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