First slide

Introduction to limits

Question

The value of $lim_{x \to \sqrt{3}} [x^{2}]$ , is

Moderate

A

3
B

2
C

9
D

non existent

Solution

We have,
$lim_{x \to {\sqrt{3}}^{-}} [x^{2}] = lim_{h \to 0} [(\sqrt{3} - h)^{2}] = 2$
and, $lim_{x \to {\sqrt{3}}^{+}} [x^{2}] = lim_{h \to 0} [(\sqrt{3} + h)^{2}] = 3$
Clearly, $lim_{x \to {\sqrt{3}}^{-}} [x^{2}] \neq lim_{x \to {\sqrt{3}}^{+}} [x^{2}]$
Hence, $lim_{x \to \sqrt{3}} [x^{2}]$ does not exist.

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