NCERT Solutions Class 12 Maths Chapter 5 Continuity and Differentiability

NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability explains the fundamental concepts of continuity of functions, their differentiability, and the relation between both of them. There are various aspects of nature that exhibit the property of continuity like the continuously flowing rivers, time in human life, and so on. Likewise, in mathematics, the notion of the continuity of a function is applied in various situations. Continuity of a function is the characteristic of a function by virtue of which, the graphical form of that function is a continuous wave. A differentiable function is a function whose derivative exists at each point in its domain. The concept of continuity and differentiability is studied in advanced mathematics and has multiple applications in engineering, science, economics, etc. Thus, it is crucial to gain a deep understanding of this topic.

NCERT Solutions Class 12 Maths Chapter 5 is helpful in building a clear understanding of the various aspects of limits, continuity of functions, their derivatives, properties, and methods to find derivatives. Some of the important topics explained in this chapter are derivatives of the specific standard function, logarithmic differentiation, derivatives of functions in parametric forms, and second-order derivatives. With the regular practice of Class 12 Maths NCERT Solutions Chapter 5, students will quickly gain a deep understanding of this topic. To learn and practice with NCERT Solutions Chapter 5 Continuity and Differentiability, download the exercises provided in the links below.

• NCERT Solutions Class 12 Maths Chapter 5 Ex 5.1
• NCERT Solutions Class 12 Maths Chapter 5 Ex 5.2
• NCERT Solutions Class 12 Maths Chapter 5 Ex 5.3
• NCERT Solutions Class 12 Maths Chapter 5 Ex 5.4
• NCERT Solutions Class 12 Maths Chapter 5 Ex 5.5
• NCERT Solutions Class 12 Maths Chapter 5 Ex 5.6
• NCERT Solutions Class 12 Maths Chapter 5 Ex 5.7
• NCERT Solutions Class 12 Maths Chapter 5 Ex 5.8
• NCERT Solutions Class 12 Maths Chapter 5 Miscellaneous Exercise

NCERT Solutions for Class 12 Maths Chapter 5 PDF

NCERT Solutions for Class 12 Maths Chapter 5 are meticulously formulated guides that promote the fundamental understanding of the representation of continuity and differentiability of functions along with their applications. To practice with these solutions, click on the links of the pdf files given below.

☛ Download Class 12 Maths NCERT Solutions Chapter 5 Continuity and Differentiability

NCERT Class 12 Maths Chapter 5  Download PDF

NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability

NCERT solutions Class 12 Maths Chapter 5 Continuity and Differentiability are highly competent guides that impart the foundational knowledge of calculus. These reliable learning resources deliver a clear sense of geometric interpretation of continuity and the differentiability of functions. The pattern followed by these solutions is quite amiable for performing a deep study of all topics. To practice the exercise-wise NCERT Solutions Class 12 Maths Continuity and Differentiability, try the exercise-wise links given below.

• Class 12 Maths Chapter 5 Ex 5.1 - 34 Questions
• Class 12 Maths Chapter 5 Ex 5.2 - 10 Questions
• Class 12 Maths Chapter 5 Ex 5.3 - 15 Questions
• Class 12 Maths Chapter 5 Ex 5.4 - 10 Questions
• Class 12 Maths Chapter 5 Ex 5.5 - 18 Questions
• Class 12 Maths Chapter 5 Ex 5.6 - 11 Questions
• Class 12 Maths Chapter 5 Ex 5.7 - 17 Questions
• Class 12 Maths Chapter 5 Ex 5.8 - 6 Questions
• Class 12 Maths Chapter 5 Miscellaneous Ex - 23 Questions

☛ Download CBSE Class 12 Maths Chapter 5 NCERT Book

Topics Covered: The main topics covered in NCERT Solutions Class 12 Maths Chapter 5 are continuity, differentiability, exponential, logarithmic functions, logarithmic differentiation, derivatives of functions in parametric forms, second-order derivative, and mean value theorem. Each of these topics is elaborated efficiently with interactive illustrations to help students grasp them better.

Total Questions: Class 12 Maths Chapter 5 Continuity and Differentiability has 144 questions in 9 exercises which are mostly short answer type questions. The sums provided in each exercise of these solutions competently cover all important topics from an exam point of view.

List of Formulas in NCERT Solutions Class 12 Maths Chapter 5

Continuity and Differentiability are the basic topics in studying calculus. Building a precise understanding of these concepts will help in learning a higher branch of mathematics called “Analysis”. To learn the continuity of functions and their derivatives it is required to have a clear knowledge of important theorems, definitions, formulas, and rules. NCERT Solutions Class 12 Maths Chapter 5 elaborates each of them with the help of examples. Some of the important terms and formulas explained in these NCERT Solutions for Class 12 Maths Chapter 5 are given below.

• Continuous Function: A function is said to be a continuous function if it is continuous on the whole of its domain. A continuous function f(x) is continuous on a given interval if it is continuous at every point of the interval.

• Arithmetic of Continuous Functions: The result of arithmetic operations performed on continuous functions is continuous. i.e., if f and g are continuous functions, then

(f ± g) (x) = f(x) ± g(x) is continuous.

(f . g) (x) = f(x) . g (x) is continuous.

( f / g ) (x) = f(x ) / g(x) (wherever g(x) ≠ 0) is continuous.

• Differentiable: A function is said to be differentiable if the derivative of the function exists at all points in its domain. Particularly, if a function f(x) is differentiable at x = a, then f′(a) exists in the domain. Some derivative rules used to find the derivatives of a function are:

i) ( f ± g )′ = f′ ± g′

ii) ( fg )′ = f′g +f g′

iii) ( f/g )′ = (f′g−fg′) /g²

• Logarithmic functions: Logarithmic functions are the inverses of exponential functions. The logarithmic function y = log_ax is defined to be equivalent to the exponential equation x = a^y.