NCERT

There are several important formulas of the Continuity and Differentiability, Students can cheeck below;

1. Continuity at a point
   $\lim_{x \to a^-} f(x) = \lim_{x \to a^+} f(x) = f(a)$limx?a?f(x)=limx?a+?f(x)=f(a)

2. Derivative of basic functions:

   • $\frac{d}{dx}(x^n) = nx^{n-1}$dxd?(xn)=nxn?1

   • $\frac{d}{dx}(\sin x) = \cos x$dxd?(sinx)=cosx

   • $\frac{d}{dx}(\cos x) = -\sin x$dxd?(cosx)=?sinx

   • $\frac{d}{dx}(e^x) = e^x$dxd?(ex)=ex

   • $\frac{d}{dx}(\ln x) = \frac{1}{x}$dxd?(lnx)=x1?

3. Product Rule:
   $\frac{d}{dx}[u \cdot v] = u \cdot \frac{dv}{dx} + v \cdot \frac{du}{dx}$dxd?[u?v]=u?dxdv?+v?dxdu?

4. Quotient Rule:
   $\frac{d}{dx} \left( \frac{u}{v} \right) = \frac{v \cdot \frac{du}{dx} - u \cdot \frac{dv}{dx}}{v^2}$dxd?(vu?)=v2v?dxdu?u?dxdv?

5. Chain Rule:
   If $y = f(g(x))$y=f(g(x)), then
   $\frac{dy}{dx} = f'(g(x)) \cdot g'(x)$dxdy?=f?(g(x))?g?(x)

Students can check our Shiksha's NCERT Solutions Page for more information.

The concept of continuity is defined for a function  as a curve that is smooth and unbroken at every point in its domain. Mathematically, a function $f (x)$ is said to be continuous at a point $x = a$ if:

$\lim_ {x \to a} f (x) = f (a)$

What it means:

• The function is defined at $x = a$,

• The limit of the function exists as $x$ approaches $a$,

• And the limit is equal to the function's value at that point.

Students can check the NCERT Class 12 Maths Chapter 5 Continuity and Differentiability for better and deep understanding of the topic.

Yes, Shiksha's NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability are aligned with the latest CBSE 2025 syllabus. Our NCERT Solutions are prepared by subject experts to provide step-by-step explanations, aiding students in their preparation for their board exams. Student can access these solutions and even download the PDF for free on our website Shiksha.

Students can find well structured NCERT Solutions for Class 12 Continuity and Differentiability in PDF form. We have provided the Solution PDF for all the chapters on our pages, in the Download Free PDF Section. Students can use these NCERT Solutions PDF for their offline study, and as a good and handy resource for practice and revision.

NCERT Class 12 Maths includes Continuity and Differentiability as Chapter 6, which is one of the fundamental concepts in calculus.

• Continuity is defined for a function in a way that curve of function behaves smoothly without any breaks or jumps at a point or over an interval.
• Differentiability deal with whether a function has a defined derivative at a point, meaning it has a clear slope or tangent. 

Students can check our NCERT solutions for Continuity and Differentiability for better understanding.

Yes, We have updated our NCERT Class 12 Maths Relations and Functions solutions updated as per the latest CBSE 2025 syllabus.We have designed to provide best method of problem-solving which ensures better scoring capabilty of students.These updated solutions help students to do self-preparation, and give confidence while solving board exam questions.

Students can find accurate NCERT Solutions for Class 12 Maths Relations and Functions on our website Shiksha.com. We provide step-by-step explanations that are easy to understand and follow the latest CBSE 2025 syllabus and exam pattern. Whether Students are preparing for board exams orfor Compeptive exams, these solutions help build a strong conceptual understanding.

Students can download the free Class 11 Limits and Derivatives NCERT Solutions PDF from our website Shiksha, which offers chapter-wise and exercise-wise solutions. These PDFs are available for free and students can access  and download it to use it offline. Studernts can access the PDF directly on the Limits and Derivatives NCERT Solutions page provided by Shiksha as a part of class 11 chapter-wise matgh solutions.

Yes,  NCERT Solutions for Limits and Derivatives are a good resource and sufficeint to build a strong foundation. Students are aware all of the class 11 maths exams will be taken based on Class 11 CBSE Exams. Our Class 11 Math Limits and Derivatives Solutions are aligned with the latest CBSE 2025 syllabus. Student can rely on these solutions ans use them to practice, revise, and make notes.

The NCERT Solutions for Class 11 Limits and Derivatives provided by shiksha, cover all important concepts, including the definition of a limit, techniques to evaluate limits, left-hand and right-hand limits, and derivatives.  Our NCERT Solutions provide step-by-step explanations to questions . Our Solutions also include basic derivative formulas, rules, and their application to simple algebraic and trigonometric functions in solutions to make students aware of their usage.