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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).
Evaluate the below given limit. Solution Note as well that we actually do have to do the right-hand limit here. We know that the natural logarithm is just described fo
if 1/x+2, 1/x+3, 1/x+5 are in AP find x Ans 1/x+2,1/x+3, 1/x+5 are in AP find x. 1/x+3 - 1/x+2 = 1/x+5-1/x+3 => 1/x 2 +5x+6 = 2/ x 2 +8x +15 => On solving we get x
Concrete Operational Stage : Piaget describes a five-year-old boy playing with a collection of pebbles. First, he laid them in a line and counted along the line from left to righ
Explain Basic Concepts of Parallel Lines ? Parallel lines are defined in section 1.2 and we use "//" to denote it. From the definition, we can get the following two consequenc
If α,β are the zeros of a Quadratic polynomial such that α + β = 24, α - β = 8. Find a Quadratic polynomial having α and β as its zeros.
Evaluate the given limit. Solution : It is a combination of many of the functions listed above and none of the limited are violated so all we have to do is plug in x = 3
A circle touches the side BC of a triangle ABC at P and touches AB and AC when produced at Q and R. Show that AQ= 1/2 (perimeter of triangle ABC) Ans: Since the length o
Do you have to pay.
Ask question #Minimum 1Let X be a topological space, let p ? X, and let F and ? be C-valued functions on X that are continuous at p. Then the functions F + ?, F?, |F|, ReF and ImF
Determining the Laplace transform of a function is not terribly hard if we've found a table of transforms opposite us to use as we saw in the previous section. What we would want t
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