Definite Integrals
Differentiation deals with the rate of change while integration deals with the total change. The definite integrals are evaluated in problems relating to plane, areas, areas and volumes of solid of revolution etc. In this chapter, we confine ourselves to proper..
Relation Between Continuity and Differentiability
The following theorem say 'Differentiability implies continuity..
Rate of Change of Quantity
If a quantity y varies with respect to another quantity 'x' satisfying some rule y = f(x), in other words if y is a function x, then represents the rate of change of y with respect to x For x = x 0 , dy/dx at x 0 is called the rate of change of y with respect to x at x 0 . If y ..
If a quantity y varies with respect to another quantity 'x' satisfying some rule y = f(x), in other words if y is a function x, then represents the rate of change of y with respect to x For x = x 0 , dy/dx at x 0 is called the rate of change of y with respect to x at x 0 . If y ..Solution of a differential equation:
A functional relation between x and y which satisfies the given differential equation. Solution of a differential equation by the method of variables separable..
Definition 4:
The functional relation-ship between the independent variable and the dependent variable (such as y = f(x)) which satisfies the given differential equaion is called the solution of the differential equatio..
Introduction
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 scienc..
Example 2:
The decay rate of radium at any point t is proportional to its mass at that time. The mass is M 0 at time t = 0. Form the differential equation and find the time when the mass will be halve..
Conclusion
In this chapter we have learnt the application of derivatives to rate measure, also we have used the geometrical measurement of dy/dx to find the equations of the tangent and normal to a curve at any point on the curve, angle of intersection of the curves...
Examples:
Derivatives are also used to trace the graphs of different functions. To optimise the value of a differentiable function of practical use, derivatives of the functions are applied. This chapter reveals with many more application of derivatives such as determining the relative error in me..
Example 1:
A wet porous substance in the open air loses its moisture at the rate proportional to the moisture content. If a sheet hung in the wind loses half of its moisture during the first hour, when will it have lost? (i) 95% moisture, weather condition remaining constant (ii) 90% moisture, weat..
See what our Users say :
She should be the head of Tutor Vista. She knows how to treat her students. Her teaching style is spectacular.
I like the way this tutors double check the work with me and took time to explain each detail. It really helped me to better understand - Harry
this tutoring helped me with each and every problem i needed help with and helped me to understand the math - ben
Wonderful session, i really enjoy this tutor, he takes his time to explain and always ask question to see if information is understood-kathy
Looking for More Help!
