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-
(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 of “f” at b means,
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.
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 :-
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