On The Floor

Calculus Level 3

Evaluate

$\large \lim_{x \to 3^-} x \left \lfloor x^2 \right \rfloor$

Notation: $\lfloor \cdot \rfloor$ denotes the floor function.

6 24 It can't be evaluated 27 None of the other answers

1 solution

Chew-Seong Cheong
May 1, 2017

$\begin{aligned} L & = \lim_{x\to 3^-} x \left \lfloor x^2 \right \rfloor \\ & = 3 \left \lfloor 9^-\right \rfloor \\ &=3(8) \\ &=\boxed{24}\end{aligned}$

what does the line next to the 3 mean?

Barry Leung - 1 year, 9 months ago

It is a minus $-$ sign which means we approach $\to$ from $< 3$ side, that is $2.99999999999...$ . If $3^+$ , it means from $> 3$ side that is $3.0000000...1$ .

Chew-Seong Cheong - 1 year, 9 months ago

On The Floor

1 solution

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