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STD 12 - 5. continuity and differentiation — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 5. continuity and differentiation4 Marks
MCQ
The function $f(x) = |x| + \frac{{|x|}}{x}$ is
  • A
    Continuous at the origin
  • B
    Discontinuous at the origin because $|x|$ is discontinuous there
  • ✓
    Discontinuous at the origin because $\frac{{|x|}}{x}$ is discontinuous there
  • D
    Discontinuous at the origin because both $|x|$ and $\frac{{|x|}}{x}$ are discontinuous there
✓

Answer

Correct option: C.
Discontinuous at the origin because $\frac{{|x|}}{x}$ is discontinuous there
c
(c) $|x|$ is continuous at $x = 0$ and $\frac{{|x|}}{x}$ is also discontinuous at $x = 0$

$\therefore $ $f(x) = \,|x| + \frac{{|x|}}{x}$ is discontinuous at $x = 0$.

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