Question:
The number of discontinuity of the greatest integer function $f\left(x\right)=\left[x\right], \, x\in \left(- \frac{7}{2} , \, 100\right)$ is equal to
The number of discontinuity of the greatest integer function $f\left(x\right)=\left[x\right], \, x\in \left(- \frac{7}{2} , \, 100\right)$ is equal to
Updated On: Jul 28, 2022
- 104
- 102
- 101
- 103
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The Correct Option is D
Solution and Explanation
Given, $f\left(x\right)=\left[x\right], \, x\in \left(- 3.5 , \, 100\right)$
As we know greatest integer is discontinuous on integer values.
In given interval, the integer values are
$\left(\right.-3, \, -2, \, -1, \, 0, \, \ldots , \, 99\left.\right)$
$\therefore $ Total numbers of integers are 103.
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Concepts Used:
Continuity & Differentiability
Definition of Differentiability
f(x) is said to be differentiable at the point x = a, if the derivative f ‘(a) be at every point in its domain. It is given by
Definition of Continuity
Mathematically, a function is said to be continuous at a point x = a, if
It is implicit that if the left-hand limit (L.H.L), right-hand limit (R.H.L), and the value of the function at x=a exist and these parameters are equal to each other, then the function f is said to be continuous at x=a.
If the function is unspecified or does not exist, then we say that the function is discontinuous.