NCERT Solutions Class 12 Mathematics Chapter 5 Continuity and Differentiability have been provided below and is also available in Pdf for free download. The NCERT solutions for Class 12 Mathematics have been prepared as per the latest syllabus, NCERT books and examination pattern suggested in Class 12 by CBSE, NCERT and KVS. Questions given in NCERT book for Class 12 Mathematics are an important part of exams for Class 12 Mathematics and if answered properly can help you to get higher marks. Refer to more Chapter-wise answers for NCERT Class 12 Mathematics and also download more latest study material for all subjects. Chapter 5 Continuity and Differentiability is an important topic in Class 12, please refer to answers provided below to help you score better in exams

## Chapter 5 Continuity and Differentiability Class 12 Mathematics NCERT Solutions

Class 12 Mathematics students should refer to the following NCERT questions with answers for Chapter 5 Continuity and Differentiability in Class 12. These NCERT Solutions with answers for Class 12 Mathematics will come in exams and help you to score good marks

### Chapter 5 Continuity and Differentiability NCERT Solutions Class 12 Mathematics

**Exercise 5.1**

**Question. Prove that the function f (x) = 5x – 3 is continuous at x = 0, at x = – 3 and at x = 5.
Answer :**

The given function is f(x) = 5x - 3

At x = 0, f(0) = 5× 0 -3 = -3

**Question. Examine the continuity of the function f (x) = 2x ^{2} – 1 at x = 3.
Answer :**

The given function is f(x) = 2x

^{2}- 1

**Question. Examine the following functions for continuity.
(i) f(x) = x - 5
(ii) f(x) = [1/(x- 5)] , x ≠ 5
(iii) f(x) = (x**

^{2}- 25)/(x + 5), x ≠ - 5 (iv) f(x) = |x - 5|, x ≠ 5 Answer :

(i) The given function is f(x) = x - 5

It is evident that f is defined at every real number k and its value at k is k - 5 .

It is also observed that

Hence, f is continuous at every real number and therefore, it is a continuous function.

(ii) The given function is f(x) = [1/(x- 5)] , x ≠ 5

For any real number k ≠ 5, we obtain

Hence, f is continuous at every point in the domain of f and therefore, it is a continuous function.

(iii) The given function is f(x) = (x^{2} - 25)/(x + 5), x ≠ - 5

For any real number c ≠ - 5 , we obtain

Hence, f is continuous at every point in the domain of f and therefore, it is a continuous function.

Therefore, f is continuous at all real numbers greater than 5.

Hence, f is continuous at every real number and therefore, it is a continuous function

**Question. Prove that the function f(x) = x ^{n} is continuous at x = n, where n is a positive integer.
Answer :**

The given function is f(x) = x

^{n}

It is evident that f is defined at all positive integers, n, and its value at n is n

^{n}.

**Question. Is the function f defined by f(x) =**

** **

**continuous at x = 0? At x = 1? At x = 2?**

Answer :

**Question. Find all points of discontinuity of f, where f is defined by **

**Answer :**

It is evident that the given function f is defined at all the points of the real line.

Let c be a point on the real line. Then, three cases arise.

c < 2

c > 2

c = 2

**Case I :** c < 2

f(c) = 2c + 3

Then,

It is observed that the left and right hand limit of f at x = 2 do not coincide.

Therefore, f is not continuous at x = 2 .

Hence, x = 2 is the only point of discontinuity of f.

NCERT Solutions Class 12 Mathematics Chapter 1 Relations and Functions |

NCERT Solutions Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions |

NCERT Solutions Class 12 Mathematics Chapter 3 Matrices |

NCERT Solutions Class 12 Mathematics Chapter 4 Determinants |

NCERT Solutions Class 12 Mathematics Chapter 5 Continuity and Differentiability |

NCERT Solutions Class 12 Mathematics Chapter 6 Application of Derivatives |

NCERT Solutions Class 12 Mathematics Chapter 7 Integrals |

NCERT Solutions Class 12 Mathematics Chapter 8 Application of Integrals |

NCERT Solutions Class 12 Mathematics Chapter 9 Differential Equations |

NCERT Solutions Class 12 Mathematics Chapter 10 Vector Algebra |

NCERT Solutions Class 12 Mathematics Chapter 11 Three Dimensional Geometry |

NCERT Solutions Class 12 Mathematics Chapter 12 Linear Programming |

NCERT Solutions Class 12 Mathematics Chapter 13 Probability |

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### NCERT Solutions Class 12 Mathematics Chapter 5 Continuity and Differentiability

NCERT Solutions Class 12 Mathematics Chapter 5 Continuity and Differentiability is available on our website www.studiestoday.com for free download in Pdf. You can read the solutions to all questions given in your Class 12 Mathematics textbook online or you can easily download them in pdf.

### Chapter 5 Continuity and Differentiability Class 12 Mathematics NCERT Solutions

The Class 12 Mathematics NCERT Solutions Chapter 5 Continuity and Differentiability are designed in a way that will help to improve the overall understanding of students. The answers to each question in Chapter 5 Continuity and Differentiability of Mathematics Class 12 has been designed based on the latest syllabus released for the current year. We have also provided detailed explanations for all difficult topics in Chapter 5 Continuity and Differentiability Class 12 chapter of Mathematics so that it can be easier for students to understand all answers.

**NCERT Solutions Chapter 5 Continuity and Differentiability Class 12 Mathematics**

Class 12 Mathematics NCERT Solutions Chapter 5 Continuity and Differentiability is a really good source using which the students can get more marks in exams. The same questions will be coming in your Class 12 Mathematics exam. Learn the Chapter 5 Continuity and Differentiability questions and answers daily to get a higher score. Chapter 5 Continuity and Differentiability of your Mathematics textbook has a lot of questions at the end of chapter to test the students understanding of the concepts taught in the chapter. Students have to solve the questions and refer to the step-by-step solutions provided by Mathematics teachers on studiestoday to get better problem-solving skills.

**Chapter 5 Continuity and Differentiability Class 12 NCERT Solution Mathematics**

These solutions of Chapter 5 Continuity and Differentiability NCERT Questions given in your textbook for Class 12 Mathematics have been designed to help students understand the difficult topics of Mathematics in an easy manner. These will also help to build a strong foundation in the Mathematics. There is a combination of theoretical and practical questions relating to all chapters in Mathematics to check the overall learning of the students of Class 12.

**Class 12 NCERT Solution Mathematics Chapter 5 Continuity and Differentiability**

NCERT Solutions Class 12 Mathematics Chapter 5 Continuity and Differentiability detailed answers are given with the objective of helping students compare their answers with the example. NCERT solutions for Class 12 Mathematics provide a strong foundation for every chapter. They ensure a smooth and easy knowledge of Revision notes for Class 12 Mathematics. As suggested by the HRD ministry, they will perform a major role in JEE. Students can easily download these solutions and use them to prepare for upcoming exams and also go through the Question Papers for Class 12 Mathematics to clarify all doubts

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