MHT CET · Maths · Continuity and Differentiability
The number of discontinuities of the greatest integer function \(\mathrm{f}(x)=[x], x \in\left(-\frac{7}{2}, 100\right)\)
- A 104
- B 100
- C 102
- D 103
Answer & Solution
Correct Answer
(D) 103
Step-by-step Solution
Detailed explanation
\(\begin{aligned}
& \mathrm{f}(x)=[x] \\
& x \in\left(\frac{-7}{2}, 100\right) \\
& x \in(-3.5,100)
\end{aligned}\)
As we know greatest integer is discontinuous on integer values in given interval, the integer values are \(\{-3,-2,-1,0 \ldots 99\}\)
\(\therefore \quad\) Total number of discontinuities are 103 .
& \mathrm{f}(x)=[x] \\
& x \in\left(\frac{-7}{2}, 100\right) \\
& x \in(-3.5,100)
\end{aligned}\)
As we know greatest integer is discontinuous on integer values in given interval, the integer values are \(\{-3,-2,-1,0 \ldots 99\}\)
\(\therefore \quad\) Total number of discontinuities are 103 .
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