Chapter 5 of Class 12 Maths named continuity and differentiability is fundamentally an extension of our education of differentiation of functions in Class XI. We had studied how to differentiate positive functions like polynomial functions and trigonometric functions. This time we familiarize ourselves with the very significant concepts of continuity at chapter 5 maths class 12, differentiability, and relations between them. We will also study the differentiation of inverse trigonometric functions. Further, we familiarize a new class of functions named exponential and logarithmic functions. To learn this chapter well you would definitely need the ncert solutions for class 12 maths chapter 5.
Basic fundamentals of Continuity
In theoretical mathematics, a function is known as a continuous function when it does not have any abrupt variations in value, known as discontinuities. In easier words, a sufficiently small variation in the input of a continuous function ends up in a randomly small fluctuation in its output. Else, a function is known as a discontinuous function. While a continuous function with a constant inverse function is referred to as homeomorphism. Continuity of functions is one of the essential ideas of topology, which got treated as a full generalization. To understand the theory and its applications in real life clearly, you must learn the basic formulas provided in the textbook, moreover, you have to learn how to read the forms of any given functions and how to identify one in a manner so that you can understand how to deal with it. Before you understand this topic in a way that you became elite at it, you must learn to solve the problems from the given exercises. To do so you may need to consult some pro-level continuity and differentiability class 12 ncert solutions, using which you can study and practice better. To find the best reference materials related to this topic you can search over the internet for continuity and differentiability class 12 related CBSE Notes study materials and practice sets.
Basic Fundamental of Differentiable function
In the theory of Calculus, a differentiable function or differentiability of a function of one real variable is a function whose derivative is real at each point in its domain. As a result, the graph of any differentiable function always has a non-vertical or tangent line at each of the interior points in its domain where the variable is real. In each case, the point is relatively smooth, and cannot comprise any breaks, bends, or cusps. If we talk in mathematical terms then, if x0 is an internal point in the domain of a given function f, then f is known to be differentiable at x0 if the derivative f ′(x0) exists in real numbers. In easier words, it would mean that the graph of f would have a non-vertical tangent line at the point (x0, f(x0)). The function f may also be identified as locally linear at x0, as it can be well approached by a linear function near this point. So, you can see the basics of Calculus begins here with quiet core and complex concepts like the above. So, to study this kind of topic in a manner that suits you to the depth of the idea and become a master at it, you would need external assistance from experienced teachers rather than a textbook. Your school teachers can not be with you while you are studying, so having prepared study materials and solutions prepared by experienced teachers are very necessary for any student like you. So, search for the best ncert solutions for class 12 maths chapter 5 pdf online to guide you.
Why to learn continuity and differentiability
The chapter of continuity and differentiability is not just important, it is career-changing. It is hard to say that how much of the use of these theories and practical you are going to have in your life, but if you are interested in higher studies related to physics, maths, computer science, IT, or Engineering then you are going to need these theories and knowledge at each step of your further studies. Apart from that to score a good mark in the XII board exam there are no better subjects than maths itself. And in maths of class XII, Calculus is so important that almost 50% of the problems in the paper are going to be from Calculus related to topics. Without studying Calculus no one would be able to score a good mark in the XII board exam in Maths paper. So, consider our ncert solutions for class 12 maths continuity and differentiability pdf files as your study reference, for optimum quality exam preparation.
What are the usages of continuity and differentiability?
The usages of continuity and differentiability or the so-called Calculus are endless. Though most time you can not see the direct impacts of the Calculus application, believe me, there are many things around you which is connected to your daily life where the Calculus theories are being used. Electronics engineering, electrical engineering, computer engineering all are directly using calculus theories because of solving various kinds of problems. No matter it is an electronic circuit or a high voltage transformer, or a big data algorithm, all use the calculus theories and implies the practical usages of calculus. To study Calculus you would need to devote a huge amount of time, labor, dedication, and focus, and also elite level guidance is need for the same. In Vedantu the expert teacher who has Subject Matter Expertise over the topic of Calculus has prepared the ncert solutions for class 12 maths to provide you the best guidance on what they, to secure your better future. To become an expert at the topic of Calculus, complete your Maths syllabus as soon as possible and then collect as many reference books as you can on the topic. Also do consider the high-quality pdf online to practice more and more, to become a pro the topic of Calculus. While doing so you will be by default prepared for the XII maths exam as well the JEE Advanced exams. So, no matter what you do at the XII science school do not even think about neglecting the Calculus.
How Vedantu can make you a pro at Calculus
You can consider the Vedantu provided online study materials first. Once you have gone through them thoroughly you will gain quite a basic knowledge of the topic. Then you can consider taking the Vedantu classes online for best care over the subject. You can find all the continuity and differentiability solved problems for your NCERT syllabus from your textbook, but in reality, that is not enough for your future preparation and for your JEE preparation. On the Vedantu website, you will not only find the solutions for exercise 5.1 class 12 maths but also the best quality future care from the experienced teacher from around the country’s best institutes. You can get all the study materials and solutions as pdf files for free to download, consider those files first to judge the quality and the effect on your study, and then you can decide how much Vedantu services are going to be helpful for you and your preparation. Remember Calculus is not a topic to study and pass in the exam, it is a skill to learn for many of your future endeavors, and quite a hard skill to learn, so study well.