First slide

Introduction to limits

Question

$lim_{x \to 3} ([x - 3] + [3 - x] - x)$ where [·]denotes the greatest integer function, is equal to

Moderate

A

4
B

-4
C

0
D

none of these

Solution

We have,
$\begin{array}{l} [x + 3] + [3 - x] = [x - 3] + [- (x - 3)] \\ = [x - 3] - [x - 3] - 1 = - 1 \\ ∴ lim_{x \to 3} ([x - 3] + [3 - x] - x) = lim_{x \to 3} (- 1 - x) = - 4 \end{array}$

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