- #1
suyver
- 248
- 0
I was wondering something that is so simple that it baffled me...
When I have the equation
[tex]a x^2+b x+c=0[/tex]
this obviously has the solutions
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
And when I have the equation
[tex]b x+c=0[/tex]
this has the solution
[tex]x=\frac{-c}{b}[/tex]
My problem now is the limiting case [itex]a\rightarrow 0[/itex] in the upper situation:
[tex]\lim_{a\rightarrow 0}\frac{-b\pm\sqrt{b^2-4ac}}{2a}\rightarrow -\infty\neq\frac{-c}{b}[/tex]
So what's wrong here? Why does this limit not exist?
When I have the equation
[tex]a x^2+b x+c=0[/tex]
this obviously has the solutions
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
And when I have the equation
[tex]b x+c=0[/tex]
this has the solution
[tex]x=\frac{-c}{b}[/tex]
My problem now is the limiting case [itex]a\rightarrow 0[/itex] in the upper situation:
[tex]\lim_{a\rightarrow 0}\frac{-b\pm\sqrt{b^2-4ac}}{2a}\rightarrow -\infty\neq\frac{-c}{b}[/tex]
So what's wrong here? Why does this limit not exist?