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Obligatoriske oppgaver for uke 3

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Det er gitt en funksjon $f(x)=\\sin x$

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Grafen til $f(x)=\\sin x$ er tegnet i grønt, og grafen til Taylor-polynomet til $f$ av grad $n$ er tegnet i orange. For hver graf skal du avgjøre hva $n$ er.

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Det er gitt en funksjon $f(x)=e^{\\var{k}x}$.

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Finn Taylor-polynomet av grad 4 til $f(x)$ i punktet $a=0$.

$p_nf(x)=$ [[0]] $+$ [[1]] $+$ [[2]] $+$ [[3]] $+$ [[4]]

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Gitt en funksjon $f(x,y)=x^2-\\cos y$

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Differensialet til $f$ blir

$df=$ [[0]]$dx$ + [[1]]$dy$

Gitt en funksjon $f(x,y)=e^{\\var{a}x}\\cdot \\sin(\\var{b}y)$ og et punkt $a=\\Big(0,\\dfrac{\\pi}{2}\\Big) $

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Taylorpolynomet av grad 2 blir da

$P_2(x,y)=$[[0]]$+$[[1]] $x+$[[2]]$(y-\\frac{\\pi}{2})+$[[3]]$x^2+$[[4]]$x(y-\\frac{\\pi}{2})+$[[5]]$(y-\\frac{\\pi}{2})^2$

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5 minutter igjen

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