OP Malhotra Continuity and Differentiability of Functions S.Chand ISC Class-12 Maths Solutions Ch-7

OP Malhotra Continuity and Differentiability of Functions S.Chand ISC Class-12 Maths Solutions Ch-7. Step by step Solutions of OP Malhotra SK Gupta, Anubhuti Gangal S.Chand ISC Class-12 Mathematics with Exe-7 and Chapter Test Questions. Visit official Website CISCE for detail information about ISC Board Class-12 Mathematics.

OP Malhotra Continuity and Differentiability of Functions S.Chand ISC Class-12 Maths Solutions Ch-7

Class: 12th
Subject: Mathematics
Chapter  : Ch-7 Continuity and Differentiability of Functionsof Section -A
Board ISC
Writer  OP Malhotra, SK Gupta, Anubhuti Gangal
Publications S.Chand Publications 2020-21

-: Included Topics :- 

Exe-7

Chapter Test


OP Malhotra Continuity and Differentiability of Functions S.Chand ISC Class-12 Maths Solutions Ch-7

 Continuity :

(i) The continuity of a real function (f) on a subset of the real numbers is defined when the function exists at point c and is given as-

continuity and 1

(ii) A real function (f) is said to be continuous if it is continuous at every point in the domain of f.

Consider a function f(x), and the function is said to be continuous at every point in [a, b] including the endpoints a and b.

Continuity of “f” at a means,

continuity and 2

Continuity of “f” at b means,

cotinuity and 3

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 = lim𝑥𝑎𝑓(𝑥) and RHL = lim𝑥𝑎+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.


Exe-7

Continuity and Differentiability of Functions S.Chand ISC Class-12 Maths Solutions Ch-7

Question 1:

Examine the continuity of the function

f(x) = 2x² – 1 at x = 3.

Question 2:

Examine the following function for continuity:

………………….

…………………..

Question 3:

…………………………

…………………………

…………………………

Question 12:

Examine the continuity of the following function :

………………….

…………………..

Question 13:

……………………..

…………………….

Question 26:

Show that the function

…………………….

Question 27:

Show that f (x) = |x – 20| is continuous at x = 20 but f'(x) does not exit at x = 20 but f ‘ (x) does not exit at x + 20.


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.

Chapter Test

OP Malhotra Continuity and Differentiability of Functions S.Chand ISC Class-12 Maths Solutions Ch-7

Question 1:

Discuss the continuity of the function defined as under :

……………………

Question 2:

For what  value of k ………………… defined by

……………………

Question 3:

………………………

……………………….

Question 7:

The function is defined by

…………………

is continuous at x = 2. Determine the value of k.

-: End of Continuity and Differentiability of Functions OP Malhotra S. Chand ISC Class-12 Maths Chapter-7 Solution :-

Return to :-  OP Malhotra S. Chand ISC Class-12 Maths Solutions


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2 thoughts on “OP Malhotra Continuity and Differentiability of Functions S.Chand ISC Class-12 Maths Solutions Ch-7”

  1. sir I NEED (i)PDF ans(ii) book format OF solutions book of s chand xii ics MATHS.is it free or have to pay for it?what cost?

    Reply

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