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Homework Statement
[tex]\frac{\infty}{\sqrt{\infty}}[/tex]
I would have said it would be infinity because infinity would grow a lot faster than its square root wouldn't it?
But my friend swears the limit is equal to 1???
That's not quite a limit as expressed just yet. Try:Homework Statement
[tex]\frac{\infty}{\sqrt{\infty}}[/tex]
I would have said it would be infinity because infinity would grow a lot faster than its square root wouldn't it?
But my friend swears the limit is equal to 1???
Cool, that worked well. And took forever.To be more precise, im trying to to a Bode diagram for a simple circuit. I need to estimate |H(j[tex]\omega[/tex])| in decibels as [tex]\omega[/tex] -> [tex]\infty[/tex] and as [tex]\omega[/tex] -> 0.
The transfer function is |H(j[tex]\omega[/tex])| = [tex]\frac{\sqrt{\left(RCj[tex]\omega[/tex]\right)^{2}}}{\sqrt{\left(RCj\omega\right)^{2}+1}}[/tex]
Assuming that [itex]j^2 = -1[/itex], you have
[tex]|H(j \omega)| = \frac{ \sqrt{- R^2 C^2 \omega^2} }{ \sqrt{- R^2 C^2 \omega^2 + 1}}[/tex]
I suggest defining [itex]x = - R^2 C^2 \omega^2[/itex], so you get
[tex]\frac{\sqrt{x}}{\sqrt{x + 1}} = \sqrt{\frac{x}{x + 1}}[/tex]
and then the limits [itex]\omega \to 0, \infty[/itex] correspond to [itex]x \to 0, -\infty[/itex] respectively.
Note that even in the "informal" notation of your first post, this gives
[tex]\sqrt{\frac{-\infty}{1 - \infty}}[/tex]
and not
[tex]\frac{\infty}{\sqrt{\infty}}[/tex]
Anyhow, there are nicer tricks to calculate the limit (for example, multiply by (-x)/(-x) inside the square root).