S8.02.4.58 type of discontinuity tikx with 1/sqrt(1-cos(2x))

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SUMMARY

The discussion focuses on the function \( f(x) = \frac{1}{\sqrt{1 - \cos{2x}}} \) and its discontinuity at \( x = 0 \). Participants analyze the left and right limits of the function at this point, noting that both limits approach infinity, indicating an infinite discontinuity. The conversation also touches on the TikZ plotting code for the function, highlighting the need for clarity in defining types of discontinuities and understanding left and right limits.

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karush
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$\tiny{s8.2.4 58}$

desmos
02_2_4_58.png.png

Let
$f(x)=\dfrac{1}{\sqrt{1-\cos{2x}}}$
(a) Graph $f$ What type of discontinuity does it appear to have at 0?\\
(b) Calculate the left and right limits of $f$ at 0. \\
Do these valuesn' confirm your answer to part (a)?

doesn't the limit going to 0 infinity both + and -

what is the tikx plot code for
$\dfrac{1}{\sqrt{1-\cos{2x}}}$ {1 / sqrt(x)} is as far as I gotalso what plotted in Overleaf didn't preview here
 
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It's not clear to me what you are asking. What "types" of discontinuity are there? How is each defined?

Do you know what "left" and "right" limits are? (Since they ask about "left" and "right" of x= 0 you might want your graph to include some negative values of x.
 

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