_ x 0 x |x| + x^2 = - Vidyadip

MCQ

$\mathop {\lim }\limits_{x \to 0} \frac{x}{{|x| + {x^2}}} = $

A
$1$
B
$-1$
C
$0$
✓
Does not exist

✓

Answer

Correct option: D.

Does not exist

d
(d) $\mathop {\lim }\limits_{x \to 0 - } f(x) = \mathop {\lim }\limits_{h \to 0} \,\,\frac{{0 - h}}{{h + {h^2}}} = \mathop {\lim }\limits_{h \to 0} \,\frac{{ - 1}}{{1 + h}} = - 1$

and $\mathop {\lim }\limits_{x \to 0 + } f(x) = \mathop {\lim }\limits_{h \to 0} \,\,\frac{h}{{h + {h^2}}} = \mathop {\lim }\limits_{h \to 0} \,\frac{1}{{1 + h}} = 1$

Hence limit does not exist.

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