# A nice blend of Graphs and Limits

Calculus Level 5

The area bounded by the points lying in between the lines $$x+5=0$$ and $$x-5=0$$ satisfying the equation $$\left| \left\lfloor y \right\rfloor \right| =\left| \left\lfloor \tan ^{ -1 }{ \left\lfloor x \right\rfloor } \right\rfloor \right|$$ is A.

Consider a function $$f:R\rightarrow R$$ . The graph of the above function has an asymptote $$2y=x+2$$ . Then $$\lim _{ x\rightarrow \infty }{ { \left[ \frac { { \left[ \left( 2f\left( x \right) +1 \right) \left( 2f\left( x \right) +3 \right) \left( 2f\left( x \right) -5 \right) \left( 2f\left( x \right) -3 \right) \left( 2f\left( x \right) -1 \right) \right] }^{ \frac { 1 }{ 5 } }-f\left( x \right) }{ f\left( x \right) } \right] }^{ x\left( 2f\left( x \right) -x \right) } } =\quad { e }^{ L }$$ . Then $$\left| A\times L \right| =$$

Details and assumptions :

$$\left| . \right|$$ represents Absolute Value function .

$$\left\lfloor . \right\rfloor$$ represents Greatest Integer function .

'e' represents exponential number .

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