Find First 3 Terms of MacLaurin Series for sec(x)

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SUMMARY

The discussion focuses on finding the first three non-zero terms of the Maclaurin series for the function sec(x). Participants suggest utilizing the known Maclaurin series for cos(x) and performing long division to derive the series for sec(x). It is emphasized that the Maclaurin series is a specific case of the Taylor series centered at zero. The complexity of dividing infinite series is acknowledged, with recommendations to refer to resources like MathWorld for further clarification.

PREREQUISITES
  • Understanding of Maclaurin series and Taylor series concepts
  • Familiarity with the function sec(x) and its properties
  • Basic knowledge of calculus, particularly derivatives
  • Experience with series manipulation, including long division of series
NEXT STEPS
  • Study the derivation of the Maclaurin series for sec(x) using calculus
  • Explore the relationship between Maclaurin series and Taylor series
  • Learn about series convergence and divergence in calculus
  • Review examples of dividing infinite series for better understanding
USEFUL FOR

Students and educators in calculus, mathematicians interested in series expansions, and anyone seeking to deepen their understanding of Maclaurin series applications.

Swatch
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I have to find the first three non-zero terms in the Maclaurin series for the function sec(x).

I guess I have to use the known Maclaurin series for cos(x) and doing 1/cos(x) series with long division. I tried that but didn't get anywere close to the right answer. Could anyone please help me?
 
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Swatch said:
I have to find the first three non-zero terms in the Maclaurin series for the function sec(x).
I guess I have to use the known Maclaurin series for cos(x) and doing 1/cos(x) series with long division. I tried that but didn't get anywere close to the right answer. Could anyone please help me?

You could try checking your textbook, or googling for Maclaurin series.
 
My textbook doesn't show enough exmples on this.
 
Swatch said:
My textbook doesn't show enough exmples on this.

How many examples do you need?. You may mean that your textbook has no examples of dividing by an infinite series. That's because that is much too complicated to be of any use. How about using the definition of MacLaurin series? The derivatives get a bit complicated but that's why you are only asked for the first three non-zero terms.
 

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