GATE XE (Engineering Sciences) 2023 - Question 15

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Section: Engineering Mathematics | Marks: 1

Which one of the following functions is differentiable at ๐‘ง= 0 but NOT differentiable at any other point in the complex plane โ„‚?

  • A. ๐‘“(๐‘ง) = ๐‘ง|๐‘ง|, ๐‘งโˆˆโ„‚
  • B. ๐‘“(๐‘ง) = sin(๐‘ง), ๐‘งโˆˆโ„‚
  • C. ๐‘“(๐‘ง) = {๐‘’ 1 ๐‘ง, ๐‘งโ‰ 0 0, ๐‘ง= 0 for ๐‘งโˆˆโ„‚
  • D. ๐‘“(๐‘ง) = ๐‘’โˆ’๐‘ง2, ๐‘งโˆˆโ„‚

Answer: A. ๐‘“(๐‘ง) = ๐‘ง|๐‘ง|, ๐‘งโˆˆโ„‚

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