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Obligatoriske oppgaver for uke 3

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Hvilke av følgende funksjoner $f(x)$ er lik sin Taylorrekke $Tf(x)$ for alle $x$

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La $f(x)=\\dfrac{1}{1-x}$

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La oss finne Taylorrekka til $f(x)$ i $x=0$

\n

$f(0)=$ [[0]]

\n

$f'(x)=$ [[1]]         $f'(0)=$ [[2]]       $\\dfrac{f'(0)}{1!}=$ [[2]]

\n

$f''(x)=$ [[3]]         $f''(0)=$ [[4]]       $\\dfrac{f''(0)}{2!}=$ [[5]]

\n

$f'''(x)=$ [[6]]         $f'''(0)=$ [[7]]       $\\dfrac{f'''(0)}{3!}=$ [[8]]

\n

$f^{(n)}(x)=$ [[9]]         $f^{(n)}(0)=$ [[10]]       $\\dfrac{f^{(n)}(0)}{n!}=$ [[11]]

\n

$Tf(x)=\\sum\\limits_{n=0}^{\\infty}$ [[12]]

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5 minutter igjen

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