Exams NCERT Solutions NCERT Solutions for Class 12 Maths Exercise 5.3 Continuity and Differentiability

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Last Modified 27-01-2023

NCERT Solutions for Class 12 Maths Exercise 5.3 Continuity and Differentiability

NCERT Solutions for Class 12 Maths Exercise 5.3 Continuity and Differentiability: Continuity and Differentiability is a critical chapter in Class 12 Maths. The detailed step-wise solutions for the in-text exercise 5.3 provided in this article have been prepared by Embibe’s subject experts. Practicing these solutions gives students good exam practice and the confidence to score good marks.

Click on the topic-wise links provided in the table below to get access to the NCERT Mathematics Chapter 5 chapter-wise important questions:

Section Name	Topic Name
5.1	Continuity
5.2	Differentiability
5.3	Derivatives of Composite and Implicit Functions
5.4	Logarithmic Differentiation
5.5	Exponential and Logarithmic Functions
5.6	Derivatives of Functions in Parametric Forms
5.7	Second Order Derivative
5.8	Mean Value Theorem

In this article, we have provided detailed solutions for all the problems of exercise 5.3 of NCERT Class 12 Maths Chapter 5 Continuity and Differentiability. Moreover, Embibe also provides access to over 3300 questions from 37 different books for to help students in their exam preparations. Read on to get the NCERT Solutions for 12th Maths Exercise 5.3.

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NCERT Solutions for Class 12 Maths Exercise 5.3: Important Topics

Maths NCERT Class 12 Solutions of Exercise 5.3 Continuity and Differentiability is aimed at understanding the differentiability of some standardized functions, which also involve implicit and inverse trigonometric functions. The function whose value can be determined indirectly by using one or more independent variables is known as an Implicit Function. The chain rule can be used to find out the derivative of an inverse trigonometric function.

NCERT Solutions for Class 12 Maths Exercise 5.3: Points to Remember

We have provided some important points that are covered in NCERT Class 12 Maths Exercise 5.3 Continuity and Differentiability to help students in their exam preparations. Refer to the list below:

A real-valued function f(x) is continuous at a point ‘a’ in its domain if lim_x→af(x) = f(a). i.e. the limit of the function at x = a is equal to the value of the function at x = a.
A function f(x) is said to be continuous if it is continuous at every point on its domain.
Sum, difference, product and quotient of continuous functions are continuous, i.e., if f(x) and g(x) are continuous functions on their common domain, then f ± g, fg, f/g (g ≠ 0), kf (k is a constant) are continuous.
A function is said to be differentiable if it is differentiable at every point in its domain.
Every differentiable function is continuous, but the converse is not necessarily true.
The sum, difference, product and quotient of two differentiable functions are differentiable.
Derivatives of some standard functions:
d/dx (xⁿ) = nxⁿ⁻¹
d/dx (e^x) = e^x
d/dx (a^x) = a^xlog_ea
d/dx (log_ex) = 1/x
d/dx (log_ax) = 1/xlog_ea

Students can get more important points for NCERT Chapter 5 on Embibe for!

NCERT Solutions for Class 12 Maths: All Chapters

Students can get NCERT Solutions for all chapters of Class 12 Maths below:

Steps to Practice Unlimited 12th NCERT Mathematics Chapter-wise Mock Tests

Embibe provides personalised mock tests for every student. They can practice in their own pace and prepare themselves with ease. Below we have provided a detailed guide to taking the mock test based on latest syllabus on Embibe:

1st Step: Click on ‘Create Account‘.
2nd Step: Enter your mobile number.
3rd Step: Then select your Goal as ‘CBSE’.
4th Step: Select your Exam Name as ’12th CBSE’.
5th Step: Click Next and select your preferred language between ‘English’ and ‘Hindi’.
6th Step: Once done, click on the below-mentioned links to take the TEST.

FAQs

Q.1: How can I download the Exercise 5.3 Class 12 Maths Solutions PDF for?

Ans. Students can find detailed solutions for all the problems of Exercise 5.3 Class 12 Maths from Embibe. The links to download the solutions have been provided in this article.

Q.2: What is the weightage/marks distribution for Continuity and Differentiability Exercise 5.3 Class 12 Maths?

Ans. Unit 3 Calculus of Class 12 Maths carries a weightage of 17 marks. Along with exercise 5.3 of Continuity and Differentiability, students should also practice other topics of this chapter.

Q.3: What are the topics involved in Exercise 5.3 Class 12 Maths?

Ans. Exercise 5.3 of Class 12 Maths include Continuity, Differentiability, Derivatives of Composite and Implicit Functions, Logarithmic Differentiation, Exponential and Logarithmic Functions, Derivatives of Functions in Parametric Forms, Second Order Derivative and Mean Value Theorem.

Q.4: What are the future applications of Exercise 5.3 Class 12?

Ans. Continuity and differentiability are applied in the domains of Aerospace, Medicine and Chemistry.

Q.5: How many questions are there in Class 12 Maths NCERT Class 12 solutions for Exercise 5.3?

Ans. There are a total of 15 questions on the topic of Continuity and Differentiability (Exercise 5.3) to practice NCERT Exemplar Class 12 Maths solutions.