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STD 11 - 12. limits — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 12. limits4 Marks
MCQ
If $f(x) = \left\{ \begin{array}{l}x,\;\;{\rm{if\, }}x\,{\rm{ \,is \,rational\, }}\\ - x,\;{\rm{if \,\,}}x\,{\rm{\, is\, irrational\,}}\end{array} \right.,$ then $\mathop {\lim }\limits_{x \to 0} f(x)$ is
  • ✓
    $ 0$
  • B
    $ 1$
  • C
    $ -1$
  • D
    Indeterminate
✓

Answer

Correct option: A.
$ 0$
$\mathop {\lim }\limits_{x \to {0^ - }} f(x) = \mathop {\lim }\limits_{h \to 0} f(0 - h) = \mathop {\lim }\limits_{h \to 0} f(0 - h) = 0$
and $\mathop {\lim }\limits_{x \to {0^ + }} f(x) = \mathop {\lim }\limits_{h \to 0} f(0 + h) = \mathop {\lim }\limits_{h \to 0} - (0 + h) = 0$
$\therefore \mathop {\lim }\limits_{x \to 0} \,\,f(x) = 0 , \left( {\because \mathop {\lim }\limits_{x \to {0^ - }} f(x) = \mathop {\lim }\limits_{x \to {0^ + }} f(x)} \right)$ .

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