Question

Evaluate the limit ( [x²] - [x] ) / (x² - 1) when x tends to 1 positive .
Handwritten question is in attachment . ​

Answer 1

Step-by-step explanation:

We have,

$\tt{ \lim_{x \to1^{ + } } \frac{ [ {x}^{2} ] - [x]^{2} }{ {x}^{2} - 1} }$

$\sf{ = \lim_{h \to0 } \frac{ [ {(1 + h)}^{2} ] - [1 + h]^{2} }{ {(1 + h)}^{2} - 1} }$

$\sf{ = \lim_{h \to0 } \frac{ [ 1 + h ^{2} + 2h ] - (1)^{2} }{ 1 + h^{2} + 2h - 1} }$

$\sf{ = \lim_{h \to0 } \frac{ 1 - (1)^{2} }{ h^{2} + 2h } }$

$= \sf{0}$