document.write( "Question 1049863: let f(x)= $\"e%5E%28-x%29\"$ write down the taylor series expansion of f(x) at c=1 \n" ); document.write( "

Algebra.Com's Answer #665440 by rothauserc(4718) $\"\"$ $\"About$

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I assume you know what a Taylor series expansion is
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\n" ); document.write( "note that the first derivative of e^-x is -e^-x and the second derivative is e^-x
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\n" ); document.write( "with c = 1, the Taylor series expansion is written as
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\n" ); document.write( "1/e - ((x-1)/e) + ((x-1)^2)/2e) - ((x-1)^3)/6e) + ((x-1)^4/24e) - ((x-1)^5/120e) + ((x-1)^6/720e) + O(x-1)^7)
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\n" ); document.write( "note that we use O (big O notation) to remind us that our function has asymptotic behavior
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\n" ); document.write( "the above expansion can be written as
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\n" ); document.write( "summation of n greater than or = 0 of (((-1)^n) * (x-1)^n) / (e * n!)
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