Error Bound on Tangent Maclaurin Series

  • Thread starter Juanriq
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  • #1
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Salutations! Just checking if my logic is correct.

Homework Statement


I need to bound the error for [tex] \tan x [/tex] on [tex] [0, \frac{\pi}{2}] [/tex]


Homework Equations


[tex]
R_n(x) = \displaystyle \frac{\tan^{n+1}(\zeta)}{(n+1)!}x^{n+1}
[/tex]


The Attempt at a Solution


So...I thought that the error should go to 0 since the factorial will eventually overtake the polynomial. Then, I thought that this logic might break down since [tex] \tan x [/tex] goes to infinity on the interval. Am I overthinking this?

Thanks!
 

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