AP EAMCET · Maths · Continuity and Differentiability
Let \([t]\) represents the greatest integer not exceeding \(t\), Then the number of discontinuous points of \(\left[10^x\right]\) in \((0,10)\) is
- A \(10^{10}-1\)
- B \(10^{10}\)
- C \(10^{10}-2\)
- D \(\mathrm{e}^{10}\)
Answer & Solution
Correct Answer
(C) \(10^{10}-2\)
Step-by-step Solution
Detailed explanation
(c) Given \(0 < x < 10\) \[ \Rightarrow 1 < 10^x < 10^{10} \] Let \(0 \leq x \leq 1\) then \(\left[10^x\right]\) will have to points of discontinuity But when \(0 < x < 1\) the \([10 x]\) will have only \(\left(10^1-2\right)=8\) points of discontinuity because we are leaving…
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