Question: $\frac{\log_{2}(x + 3)}{x^{2} + 3x + 2}$, where [x] is the greatest integer less than or equal to ...

Question

$\frac{\log_{2}(x + 3)}{x^{2} + 3x + 2}$ , where [x] is the greatest integer less than or equal to x is

Answer 1

Solution

For $2 < x < 3 , \left[ \frac { x } { 3 } \right] = 0$ .

Hence $\lim _ { x \rightarrow 2 + } \left( \frac { | x | ^ { 3 } } { 3 } - \left[ \frac { x } { 3 } \right] ^ { 3 } \right) = \frac { 2 ^ { 3 } } { 3 } = \frac { 8 } { 3 }$ .

Question: \(\frac{\log_{2}(x + 3)}{x^{2} + 3x + 2}\), where [x] is the greatest integer less than or equal to ...

Solution