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.

## 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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