How to learn Calculus How to learn Calculus
Calculus is the science of mathematics in which we deals with the instantaneous change in a variable. The first question is that how to learn calculus? To understand or learn this first you must understand the concept of dy / dx. d y / d x represents this change in a variable y with respect to x. y and x both are independent variables. d(K)/dx=0 Here K is a constant. As the constant number does not change with time, the instantaneous change is 0 for a constant number. We can also define the instantaneous change in the form of limits. f ' (y) = lim h - > 0 f ( y+h ) - f ( y ) / h. The second part of calculus is Integration. The integration is exactly the reciprocal of differentiation. Once you understand the differentiation, you will easily understand the integration process and its methods. Know More About Composition Law of Limit worksheet
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For example consider the following equation, f ( x ) = y= x 2 dxn/dy =nx(n-1) Here n is number and a and y are independent variables. On differentiating the equation, we get: dy/dx=2x As I said, integration is just opposite to differentiation. So, the integration of above function will results in the same function. To represent integration we uses the symbol ‘∫’. ∫2x=x2 =f(x)=y The differentiation concept is that we consider the minute change and calculate the things for very small entities. Dy represents a very small change in the value of y. This is the basic of “what calculus is”? The calculus also deals with the trigonometric functions like sin , cos , tan, etc. The derivative part of these functions is as follows: d ( sin x ) / d x = cos x d ( cos x ) / d x = - sin x d ( tan x ) = sec 2 x These are the basic trigonometric functions. The inverse trigonometric and hyperbolic functions also have their derivatives. Read More About Composition Law of Limit worksheets
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Comparison between Integration and Differentiation Differentiation and Integration both are main roots of mathematics and even mathematics cannot be imagined without differentiation and integration. Many important branches of mathematic. Application of Integration Anti derivative of function f is the function F whose derivative is function f. We can understand it by an equation as F'=f. This process is also known as anti differentiation. This term is related to the defination. Limits in calculus Before talking about limits in calculus, one must be familiar with few basic topics of calculus like functions, range and domain. These are very important to understand the concept of math. Differentiation is Linear Differentiation is a process of finding the derivative of a function. Whenever we deal with pre-calculus or calculus we have to deal with differentiation. If we call differentiation as the heart of the calculus. Definition of Calculus Calculus is a branch of mathematics which deals with function, range, and domain. It also deals with the rate of change, infinite sequences and orbits of planet. We can find the derivative and integral of any given function with the help of calculus. It includes arithmetic, algebra, trigonometry, geometry, and coordinates geometry.
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As the constant number does not change with time, the instantaneous change is 0 for a constant number. We can also define the instantaneous...