Chapter 5 : Continuity and Differentiability - Ncert Solutions for Class 12-science Maths CBSE
Your CBSE Class 12 syllabus for Maths consists of topics such as linear programming, vector quantities, determinants, etc. which lay the foundation for further education in science, engineering, management, etc. Studying differential equations will be useful for exploring subjects such as Physics, Biology, Chemistry, etc. where your knowledge can be applied for scientific investigations.
On TopperLearning, you can find study resources such as sample papers, mock tests, Class 12 Maths NCERT solutions and more. These learning materials can help you understand concepts such as differentiation of functions, direction cosines, integrals, and more. Also, you can practise the Maths problems by going through the solutions given by our experts.
Maths is considered as one of the most difficult subjects in CBSE Class 12 Science. Our Maths experts simplify complex Maths problems by assisting you with the right methods to solve problems and score full marks. You may still have doubts while referring to the Maths revision notes or Maths NCERT solutions. Solve those doubts by asking an expert through the “Undoubt” feature on the student dashboard.
Chapter 5 - Continuity and Differentiability Exercise Ex. 5.1
The given function is f(x) = 5x - 3
At x = 0, f(0) = 5 × 0 - 3 = -3
The given function is f(x) = x2 - sinx + 5
It is evident that f is defined at x = ∏
The given function f is continuous at x = , if f is defined at x = and if the value
of f at x = equals the limit of f at x =
Chapter 5 - Continuity and Differentiability Exercise Ex. 5.2
Then, (v ο u)(x) = v(u(x)) = v(x2 + 5) = sin (x2 + 5) = f(x)
Chapter 5 - Continuity and Differentiability Exercise Ex. 5.3
Chapter 5 - Continuity and Differentiability Exercise Ex. 5.4
Chapter 5 - Continuity and Differentiability Exercise Ex. 5.5
Chapter 5 - Continuity and Differentiability Exercise Ex. 5.6
Chapter 5 - Continuity and Differentiability Exercise Ex. 5.7
Chapter 5 - Continuity and Differentiability Exercise Ex. 5.8
Rolle's theorem states that there is a point c (-4, -2) such that f'(c) = 0
then there exists some c (a, b) such that f'(c) = 0
Let n be an integer such that n (5, 9).
Let n be an integer such that n (-2, 2).
Therefore, by the Mean Value Theorem, there exists c (-5, 5) such that
Mean Value Theorem states that there is a point c (1, 4) such that f'(c) = 1
Chapter 5 - Continuity and Differentiability Exercise Misc. Ex.
where sin x > cosx
Consider the function f(x)=|x-1|+|x-2|
Since we know that the modulus function is continuous everywhere, so there sum is also continuous
Therefore, function f is continuous everywhere
Now, let us check the differentiability of f(x) at x=1,2
[Take x=1-h, h>0 such that h→0 as x→1-]
[Take x=1+h, h>0 such that h→0 as x→1+]
Therefore, f is not differentiable at x=1.
[Take x=2-h, h>0 such that h→0 as x→2-]
[Take x=2+h, h>0 such that h→0 as x→2+]
Therefore, f is not differentiable at x=2.
Hence, f is not differentiable at exactly two points.
Why CBSE Class 12 Science Maths solutions are important?
Maths is a subject which requires practising a variety of problems to understand concepts clearly. By solving as many problems as you can, you’ll be able to train your brain in thinking the logical way to solve maths problems. For practising problems, study materials such as sample papers, previous year papers, and NCERT solutions are needed.
Some of the best Maths experts work with us to give you the best solutions for Maths textbook questions and sample paper questions. Chapter-wise NCERT solutions for Class 12 Science Maths can be easily accessible on TopperLearning. Use these solutions to practise problems based on concepts such as direction ratios, probability, area between lines, inverse trigonometric functions, and more.
To prepare for your Maths exam, you need to attempt solving different kinds of Maths questions. One of the best ways to assess your problem-solving abilities is to attempt solving previous year papers with a set timer. Our Maths solutions will come in handy to help you with checking your answers and thus, improving your learning experience. So, to score more marks in your Class 12 board exams, use our Maths solutions that will enable you with the appropriate preparation.
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