Continuity and Differentiability for ISC Class-12 Maths Understanding Solutions

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Continuity and Differentiability for ISC Class-12 Maths Understanding Solutions Chapter-5. Step by step Solutions of ML Aggarwal ISC Mathematics Class-12  Exercise 5.1, Exe 5.2 And Exe 5.3, Exe 5.4, Exe 5.5, Exe 5.6, Exe 5.7, Exe 5.8, Exe 5.9, Exe 5.10, Exe 5.11, Exe 5.12, Exe 5.13, Exe 5.14, Exe 5.15, Exe 5.16 With Chapter Test Questions. Visit official Website CISCE for detail information about ISC Board Class-12 Mathematics.

ML Aggarwal Solutions of Continuity and Differentiability for ISC Class-12 Maths

Continuity and Differentiability for ISC Class-12 Maths Understanding Solutions

Board   ISC
Class  12
Subject Mathematics
Chapter-5 Continuity and Differentiability
Session  2024-25
Topics  Solutions of ML Aggarwal

Continuity and Differentiability

Continuity at a Point: A function f(x) is said to be continuous at a point x = a, if
Left hand limit of f(x) at(x = a) = Right hand limit of f(x) at (x = a) = Value of f(x) at (x = a)
i.e. if at x = a, LHL = RHL = f(a)
where, LHL = lim𝑥→𝑎–𝑓(𝑥) and RHL = lim𝑥→𝑎+𝑓(𝑥)
Note: To evaluate LHL of a function f(x) at (x = o), put x = a – h and to find RHL, put x = a + h.

Continuity in an Interval: A function y = f(x) is said to be continuous in an interval (a, b), where a < b if and only if f(x) is continuous at every point in that interval.

  • Every identity function is continuous.
  • Every constant function is continuous.
  • Every polynomial function is continuous.
  • Every rational function is continuous.
  • All trigonometric functions are continuous in their domain.

Algebra of Continuous Functions

Suppose f and g are two real functions, continuous at real number c. Then,

  • f + g is continuous at x = c.
  • f – g is continuous at x = c.
  • f.g is continuous at x = c.
  • cf is continuous, where c is any constant.
  • (𝑓/𝑔) is continuous at x = c, [provide g(c) ≠ 0]

Suppose f and g are two real valued functions such that (fog) is defined at c. If g is continuous at c and f is continuous at g (c), then (fog) is continuous at c.

If f is continuous, then |f| is also continuous.

Differentiability: A function f(x) is said to be differentiable at a point x = a, if
Left hand derivative at (x = a) = Right hand derivative at (x = a)

Exe-5.1, 

Continuity and Differentiability for ISC Class-12 Maths Understanding Solutions

Exe-5.2

 Continuity and Differentiability for ISC Class-12 Maths

Exe-5.3, 

Continuity and Differentiability for ISC Class-12 Maths Understanding Solutions

Exe-5.4, 

Continuity and Differentiability for ISC Class-12 Maths

Exe-5.5, 

Continuity and Differentiability for ISC Class-12 Maths ML Aggarwal  Solutions

Exe-5.6, 

 Continuity and Differentiability Class-12 Maths Ch-5

Exe-5.7

 Understanding ISC Class-12 Maths Ch-5

Exe-5.8

  ISC Class-12 Maths Ch-5

Exe-5.9

 ISC Class-12 Maths Ch-5

Exe-5.10 

 Solutions of Continuity and Differentiability for ISC Class-12 Maths

Exe-5.11

Understanding ISC Class-12 Maths Ch-5

Exe-5.12, 

 Continuity and Differentiability ISC Class 12 Maths

Exe-5.13

 Continuity and Differentiability ISC Class-12 Maths Ch-5

Exe-5.14, 

 Continuity and Differentiability Class-12 Maths Ch-5

Exe-5.15 

 Continuity and Differentiability ISC Class-12 Maths Ch-5

Exe-5.16

 Continuity and Differentiability ISC Class-12 Maths Ch-5

Chapter Test

 Continuity and Differentiability Understanding Class-12 Maths Ch-5

-: End of Continuity and Differentiability for ISC Class-12 Maths Understanding Solutions:-

Return to :-  ML Aggarwal Solutions for ISC Class 12 Maths Vol-1

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58 thoughts on “Continuity and Differentiability for ISC Class-12 Maths Understanding Solutions”

  6. Plz let me know how to see these solution i will be very thankful to you as in may i am going to have my maths paper so please help me out
    Thank you

    Reply

  11. Why are there no solutions for this chapter… If u don’t have then why are you making such website that just shows the exercise number and it’s page number.. We have our books for that sort of information… So 🙏, upload the answers ASAP…
    It’s an honourable request…..

    Reply

  16. It’s been more than 5 months, the solutions are still not uploaded on the site. What is the problem? How much more do we have to wait? Are the managers and developers of this site are planning to post the solutions after the board exams?

    Reply

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