# NCERT Exemplar Class 12 Maths Chapter 5 Solutions: Continuity and Differentiability

NCERT Exemplar Class 12 Maths Solutions Chapter 5 ‘Continuity and Differentiability’ are given to help you go through your entire syllabus related to this chapter to gain good marks in the final examination. These NCERT Exemplar Class 12 Maths solutions are designed as per the CBSE examination recommendations. In this chapter, there are a total of 106 exemplar problems divided into short and long answer questions, MCQs, true/false, etc.

We shall learn about the concepts of differentiability and continuity, composite functions’ derivatives, functions of opposite trigonometric, logarithmic functions and exponentials, statement of mean value, rolle’s formula. NCERT Exemplar Class 12 Maths Solutions Chapter 5 sets a benchmark for you to prepare it thoroughly and solve any type of question in the examination irrespective of its difficulty level.

Instasolv’s NCERT exemplar solutions for the chapter continuity and differentiability helps clear their basic understanding regarding this chapter as there is a probability of 10-12 marks questions from this chapter. These NCERT exemplar problems with solutions can be followed for CBSE, ICSE Board, other state boards and JEE Mains, JEE Advanced, NEET and other competitive examinations.

**Important Topics for NCERT Maths Exemplar Solutions Class 12 Chapter 5**

** Continuity: **Generally continuity is like when you create a graph without picking the nib on the paper even for a single time, but for the mathematical point of view the below-given rules have to be fulfilled such as:

- f= function = continuous when X=A ; when the graph of the function shows no breaks at a particular point then c=f(a )
- In the case of the interval, f is continuous when the total interval shows no break in the graph.
- The function of A is limited

**Discontinuity**: F= function = discontinuous at X equals to A in the given circumstances if the above conditions are not satisfied.

** Derivatives’ algebra**: suppose we have 2 differentiation functions k(x) and j(x) and the same domain. Using this formula, you will be taught how to get derivatives of given functions in Dissimilar kinds of equations.

For theorem, the meaning of the derivative of a function:

**df/dx=****Lim**_{h→0}** (f(x+h)–f(x)/h)**

** The above formula can be used to prove theorems (T)**

T 1: The derivatives of a total of any 2 functions = total of function’s derivatives

** d/ dx[k(x)+j(x)]=d/dx*k(x)+d/dx*j(x)**

T2: the derivative of variance among 2 functions = variance of function’s derivatives

**d/ dx [k(x)–j(x)]=d/dx*k(x)–d/dx*j(x)**

T3: the product rule = derivative *j(x) *k(x)

**d/ dx [k(x)*j(x)] =[d/dx*{k(x)}]*j(x)+[d/dx*{j(x)}]*k(x)**

**Power rule: ** (d/dx)*(x*r) =r*xr−1; r = real number

## Exercise Discussion of NCERT Maths Exemplar Solutions Class 12 Chapter 5

- In the given short answer questions, the questions are based on the conditions of continuity, one has to be very sure before the application of formulas. Many questions are asked with reference to trigonometric equations, the derivatives are asked to prove.
- There are certain question-based on chain rule and Rolle’s Theorem; one requires a rapid practice with such types of questions to attempt them in the final examinations. Students who are not averse with the theory of this chapter NCERT Exemplar Class 12 Maths cannot attempt all the questions, as they require thorough cramming for the rules, theorems, and practicability. Generally, students fail to get full marks from the questions asked, as these are lengthy in nature and very time consuming, so a step by step procedure is required to complete a question.
- There are 11 objective type questions which are marks fetching in nature. One option has to be checked concerning its question
- 5 questions -Fill in the blanks. There is also a question of the match the following types, and 6 questions for true/ false. Though these questions seem very easy, they need good preparation.
- Another exercise is a mixture of various questions, based on functions, algebra of derivatives, derivatives functions, mean value theorem, opposite trigonometric functions, etc.

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