NTA Abhyas 2020
Exam NTA Abhyas
Year 2020
Subject Mathematics
Chapter Continuity and Differentiability NTA Abhyas 2020 · Mathematics · Continuity and Differentiability
The function f (x) =\ x\ (π [x]),where [.] denotes the greatest...
The function \text{f} \left(\text{x}\right) =\left\{\text{x}\right\}\text\sin \left(\pi \left[\text{x}\right]\right),where [.] denotes the greatest integer function and {.} is the fractional part function, is discontinuous at
Options A all x x x B all integer points C no x x x D x x x
Step-by-step solution
f ( x ) = { x } sin ( π [ x ] ) \text{f} \left(\text{x}\right) = \left\{\text{x}\right\} \text{sin} \left(\pi \left[\text{x}\right]\right) f ( x ) = { x } sin ( π [ x ] ) = { x } s i n = \left\{x\right\}sin = { x } s in (integral multiple of
π \pi π )
= 0 = 0 = 0 Hence,
f ( x ) f ( x ) f ( x ) is continuous for all
x x x .
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