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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).
If d is the HCF of 30, 72, find the value of x & y satisfying d = 30x + 72y. (Ans:5, -2 (Not unique) Ans: Using Euclid's algorithm, the HCF (30, 72) 72 = 30 × 2 + 12
Standardizing a Random Variable If X is a random variable with E(X) = m and V(X) = s 2 , then Y = (X – m)/ s is a random variable with mean 0 and standard deviatio
Explain How to Distribute simplifying expressions? The distributive law states that for all numbers a, b, and c, a(b + c)= ab + ac What does this mean in plain language?
2x^3+5x^2+2x+5
Solve 8 cos 2 (1 - x ) + 13 cos(1 - x )- 5 = 0 . Solution Now, as specified prior to starting the instance this quadratic does not factor. Though, that doesn't mean all i
whats 2*2
QR is the tangent to the circle whose centre is P. If QA || RP and AB is the diameter, prove that RB is a tangent to the circle.
Even and Odd Functions : This is the final topic that we have to discuss in this chapter. Firstly, an even function is any function which satisfies,
1. Draw a pair of tangents to a circle of radius 2cm that are inclined to each other at an angle of 900. 2. Construct a tangent to a circle of radius 2cm from a point on the c
Solve the Extraneous Solutions ? You're worst enemy (aside from arithmetic mistakes), while you're trying to solve a rational equation, is forgetting to check for extraneous so
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