Question:
The no. of points of discontinuity of the function f (x) = x - [x] in the interval (0, 7) are
The no. of points of discontinuity of the function f (x) = x - [x] in the interval (0, 7) are
Updated On: Aug 10, 2024
- 2
- 4
- 6
- 8
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The Correct Option is C
Solution and Explanation
The graph of the function f (x) = x - [x] for the interval (0, 7) is shown below :
It is obvious from the above graph that the function x - [x] is discontinuous at the points x = 1, 2, 3, 4, 5, 6. Therefore no. of points of discontinuity of the given function in the given interval are 6.
It is obvious from the above graph that the function x - [x] is discontinuous at the points x = 1, 2, 3, 4, 5, 6. Therefore no. of points of discontinuity of the given function in the given interval are 6.
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Concepts Used:
Limits
A function's limit is a number that a function reaches when its independent variable comes to a certain value. The value (say a) to which the function f(x) approaches casually as the independent variable x approaches casually a given value "A" denoted as f(x) = A.
If limx→a- f(x) is the expected value of f when x = a, given the values of ‘f’ near x to the left of ‘a’. This value is also called the left-hand limit of ‘f’ at a.
If limx→a+ f(x) is the expected value of f when x = a, given the values of ‘f’ near x to the right of ‘a’. This value is also called the right-hand limit of f(x) at a.
If the right-hand and left-hand limits concur, then it is referred to as a common value as the limit of f(x) at x = a and denote it by lim x→a f(x).