Continuity And Differentiability Class 12 Notes Chapter 5

CBSE Class 12 Maths Chapter 5 Notes: Continuity and Differentiability

Students can refer to the short notes and MCQ questions along with separate solution pdf of this chapter for quick revision from the links below:

• Continuity and Differentiability Study Notes PDF
• Continuity and Differentiability MCQ Practice Questions PDF
• Continuity and Differentiability MCQ Practice Solutions PDF

CBSE Class 12 Maths Notes Chapter 5 Continuity and Differentiability – Related Links

• Continuity And Differentiability For Class 12
• Limits, Continuity and Differentiability – Evaluations and Examples
• Important Questions for Class 12 Maths Chapter 5 – Continuity and Differentiability

What is a Continuous Function?

When in a function, the real value at a point is said to be continuous when at that point, the function of that point is equal to the limit of the function at that point. The continuity exists when all of the domain is continuous.

The difference, product, and quotient are continuous when it comes to a continuous function. Let’s understand with the help of an example.

(f

(f.g)(x)=f(x).g(x) is again said to be continous.

(f/g)(x)=f(x)/g(x) and g(x)

All the functions which are differential are said to be continuous, but vice versa is not true.

Chain Rule

The composite of the functions can be differentiated with the help of chain rule. If f=v, t=u(x)
Then the existence of

Logarithmic Differentiation

When the differential equation is in the form

What is Rolle’s Theorem?

Let us consider a continuous function f:[a,b]

What is Mean Value Theorem?

Let us consider a continuous function f:[a,b]

Important Questions

1. If
   \(\begin{array}{l}\cos y=x\cos (a+y), with \cos a\neq \pm 1, prove \; that \frac{\partial y}{\partial x}=\cos ^{2}(a+y)/\sin a\end{array} \)
2. If
   \(\begin{array}{l}x=a(\cos t+t\sin t) and, y=a(\sin t-t\cos t), find \frac{\partial^2 y}{\partial x^2}\end{array} \)
3. If
   \(\begin{array}{l}f(x)=\left | x \right |^{3}\end{array} \)
   show that f’’(x) is available for the value of x and find it.
4. With the help of mathematical induction, prove that
   \(\begin{array}{l}\frac{\partial }{\partial x}(x^{n})=nx^{n-1}\end{array} \)
   for integers of n anf positive.
5. Obtain the same formula as cosines when
   \(\begin{array}{l}\sin (A+B)=\sin A\cos B+\cos A\sin B\end{array} \)

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