Difference between 1/x and Cosech (x) graph

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SUMMARY

The discussion focuses on the differences between the graphs of the functions 1/x and Cosech(x), specifically the hyperbolic cosecant function defined as g(x) = csch(x) = 2/(e^x - e^{-x}). Participants confirm that these two graphs are distinctly different and emphasize the importance of graphing both functions to observe their unique characteristics. The conversation highlights the necessity of visual representation and understanding the mathematical properties of these functions for accurate comparison.

PREREQUISITES
  • Understanding of hyperbolic functions, specifically Cosech(x)
  • Familiarity with the function f(x) = 1/x
  • Basic graphing skills using graphing tools or software
  • Knowledge of exponential functions and their properties
NEXT STEPS
  • Graph the functions g(x) = csch(x) and f(x) = 1/x using graphing software
  • Study the properties of hyperbolic functions, focusing on Cosech(x)
  • Analyze the asymptotic behavior of both functions as x approaches zero and infinity
  • Explore the differences in the range and domain of 1/x and Cosech(x)
USEFUL FOR

Students studying calculus, educators teaching hyperbolic functions, and anyone interested in understanding the graphical differences between rational and hyperbolic functions.

aurao2003
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Homework Statement


Hi
Can anyone tell me the difference between the 1/x and Cosech(x) graph?
Thanks



Homework Equations





The Attempt at a Solution

 
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You mean the hyperbolic cosecant?
g(x) = csch\;x = \frac{2}{e^x - e^{-x}}
Graph this and
f(x) = \frac{1}{x}
on your grapher and compare the table of values. Are they the same?
 
That's a very strange question! The two graphs are not at all the same! There are so many differences, what kind of answer are you looking for? HAVE you actually draw the graphs yourself?
 
HallsofIvy said:
That's a very strange question! The two graphs are not at all the same! There are so many differences, what kind of answer are you looking for? HAVE you actually draw the graphs yourself?
Yes! I have drawn them. But how would you explain the differences to someone without a mathematical understanding?
 
eumyang said:
You mean the hyperbolic cosecant?
g(x) = csch\;x = \frac{2}{e^x - e^{-x}}
Graph this and
f(x) = \frac{1}{x}
on your grapher and compare the table of values. Are they the same?
Thanks. My question is more in relation to a basic sketch and features.
 

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