- #1
tahayassen
- 270
- 1
[tex]\underset { x\rightarrow -\infty }{ lim } (\sqrt { { x }^{ 2 }+x+1 } +x)\\ =\underset { x\rightarrow -\infty }{ lim } (|x|\sqrt { 1+{ x }^{ -1 }+{ x }^{ -2 } } +x)\\ Since\quad x\rightarrow -\infty \\ =\underset { x\rightarrow -\infty }{ lim } (-x\sqrt { 1+{ x }^{ -1 }+{ x }^{ -2 } } +x)\\ =\underset { x\rightarrow -\infty }{ lim } x(-\sqrt { 1+{ x }^{ -1 }+{ x }^{ -2 } } +1)\\ =\underset { x\rightarrow -\infty }{ lim } x\quad *\underset { x\rightarrow -\infty }{ lim } (-\sqrt { 1+{ x }^{ -1 }+{ x }^{ -2 } } +1)\\ =\quad -\infty *0\\ =\quad 0[/tex]
Before you say that you can't multiply infinity by 0, why not? If we thinking infinity as a very large number, it doesn't matter how large it is, if it gets multiplied by 0, it will equal 0, right?
Before you say that you can't multiply infinity by 0, why not? If we thinking infinity as a very large number, it doesn't matter how large it is, if it gets multiplied by 0, it will equal 0, right?