Limits, Continuity & Differentiability
Continuity And Differentiability
nta_abhyas_2025
Grade 12
The number of discontinuity of the greatest integer function $f(x) = [x]$, $x \in (-\frac{1}{2}, 100)$ is equal to
Step-by-Step Solution
Key Concept: The greatest integer function $[x]$ is discontinuous at every integer value within the domain.
Given $f(x) = [x]$, $x \in (-3.5, 100)$. The greatest integer function is discontinuous at integer values. In the given interval, the integer values are $(-3, -2, -1, 0, \ldots, 99)$. Counting these integers: from $-3$ to $99$ inclusive, there are $99 - (-3) + 1 = 103$ integers. Therefore, the total number of integers is $103$.
Correct Answer: 103