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Continuous and differentiable Of Cos 
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#1
Dec208, 04:38 PM

P: 21

1. The problem statement, all variables and given/known data
how could i prove that cos x= sum (n=1 to 00) [((1)^n) * x^(2n)/((2n)!)] is continuous and differentiable at each x in R 2. Relevant equations the Taylor Expansion of cosine is the given equation 3. The attempt at a solution basically i need to prove that the Taylor expansion of cos is differentiable and continuous. I think i need to use the Weierstrass Mtest, however i could not figure out what M_n was, is there a different way to go about this one, or any suggestions for M_n 


#2
Dec208, 05:05 PM

P: 21

Could I choose M_n to be something like this:
Let x be any real number and let L be large enough that x is in [L, L]. Then M_n=L^(2n)/(2n)! and then use the Ratio Test to show convergence the convergence of the sum of M_n. I think I could use the Ratio Test here, but I'm not sure how. 


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