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

karush
Gold Member
MHB
Messages
3,240
Reaction score
5
$\tiny{s8.2.4 58}$

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
 
Physics news on Phys.org
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.
 
For original Zeta function, ζ(s)=1+1/2^s+1/3^s+1/4^s+... =1+e^(-slog2)+e^(-slog3)+e^(-slog4)+... , Re(s)>1 Riemann extended the Zeta function to the region where s≠1 using analytical extension. New Zeta function is in the form of contour integration, which appears simple but is actually more inconvenient to analyze than the original Zeta function. The original Zeta function already contains all the information about the distribution of prime numbers. So we only handle with original Zeta...

Similar threads

Back
Top