Derivatives

Applications of Derivatives Help:Let us understand the concept of application of derivatives help.After having studied functions, limits and continuity in the previous chapter, we shall further divide the class of continuous functions into two sub classes, derivable and non-derivable.After having studied functions, limits and continuity in the previous chapter, we shall further divide the class of continuous functions into two sub classes, derivable and non-derivable.The derivative, measures the rate at which the dependent variable changes with respect to the independent variable.










It is one of the most important ideas in Calculus. The differentiation of functions are widely used in science, economics, medicine and computer science.While studying derivatives we are faced with many questions related to application of Derivatives.The degree of a differential equation whose differential coefficients have positive integral powers is defined as the highest power(positive integral index) of the highest order derivative in it.The last but not the least concept which needs attention is application of Derivatives solved probles.We can find many solved problems related to this topic.Hope you like the above example of Derivative.Please leave your comments, if you have any doubts.

Learn Sine Rule

Let us study about sine rule in Trigonometry,

Introduction :

An equation containing the trigonometrical functions of an unknown quantity is termed as a trigonometrical equation, which holds for some values (and not for all values) of the quantities involved.
Co-terminal Angles

The angles (2p + A), (4p + A)......have the same initial and terminal arm as the angle A and so these angles are called co-terminal angles. For all such angles, the value of any trigonometric ratio is the same. Thus, all co-terminal angles are trigonometrically equivalent.

Theorem 1
General solution of sin q = k.

Theorem 2
General solution of cos q = k.

Theorem 3
General solution of tan q = k.

Theorem 4
General solution of acosq + bsinq = c.

I hope the above explanation helped you, now let me explain Cos.

Introduction of coordinate Geometry

Let us learn about coordinate Geometry,

The use of geometry dates back to before the beginning of history. However, it was often used in a very practical manner. It wasn't till about 600 BC that mathematicians began using formal logic and reasoning.

Coordinate plane--a two-dimensional surface on which a coordinate system has been set up; invented by Rene Descartes; also called Cartesian plane, graph, coordinate grid

Coordinates--the numbers in an ordered pair that locate a point in the coordinate plane

Ordered pair--a pair of numbers, written as (x,y), that represents a point on a coordinate grid

Line segment--the part of a line between two points on the line, including the two points

X-axis--the horizontal number line on a coordinate grid

Y-axis--the vertical number line on a coordinate grid

Quadrants, Origin

To plot points, always write the x value first and then the y value.

Ex. (2, 3) (3, -1) (-2, 3) (-3, -2)

Postulates and Theorems

Let us study about postulates and theorems,

A postulate is a statement that is assumed true without proof. A theorem is a true statement that can be proven. Listed below are six postulates and the theorems that can be proven from these postulates.

* Postulate 1: A line contains at least two points.

* Postulate 2: A plane contains at least three noncollinear points.

* Postulate 3: Through any two points, there is exactly one line.

* Postulate 4: Through any three noncollinear points, there is exactly one plane.

* Postulate 5: If two points lie in a plane, then the line joining them lies in that plane.

* Postulate 6: If two planes intersect, then their intersection is a line.

* Theorem 1: If two lines intersect, then they intersect in exactly one point.

* Theorem 2: If a point lies outside a line, then exactly one plane contains both the line and the point.

* Theorem 3: If two lines intersect, then exactly one plane contains both lines.

I hope the above explanation was useful

Comparing Statistical Results

Let us study how to do comparing statistical results,
Making predictions is only one use of statistics. Suppose you have recently developed a new headache/pain remedy that you call Ache-Away. Should you produce Ache-Away in quantity and make it available to the public? That would depend, among other concerns, upon whether Ache-Away is more effective than the old remedy. How can you determine that?

One way might be to administer both remedies to two separate groups of people, collect data on the results, and then statistically analyze that data to determine if Ache-Away is more effective than the old remedy. And what if the results of this test showed Ache-Away to be more effective? How certain can you be that this particular test administration is indicative of all tests of these two remedies? Perhaps the group taking the old remedy (the control group) and the group taking Ache-Away (the treatment group) were so dissimilar that the results were due not to the pain remedies but to the differences between the groups.

It's possible that the results of this test are far off the results that you would get if you tried the test several more times. You certainly do not want to foist a questionable drug upon an unsuspecting public based upon untypical test results. How certain can you be that you can put your faith in the results of your tests? You can see that the problems of comparing headache remedy results can produce headaches of their own.
Hope the above explanation was useful to you.