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Obligatoriske oppgaver for uke 3

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Hvilket av de skraverte grå områdene viser den største definisjonsmengden funksjonen $f(x,y)=\\ln(x+y)$ kan ha?

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Velg et funksjonsuttrykk for hver graf

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Hvilke av følgende funksjoner er skalarverdifunksjoner

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Finn grenseverdien 

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$\\lim\\limits_{(x,y)\\rightarrow(\\var{a},\\var{b})} x^2-3xy^2+xy-y$

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Det er gitt en funksjon $f:\\{(0,0)\\}\\cup\\{(x,y)|x\\geq5, y\\geq5\\}\\rightarrow\\mathbb{R}$

\n

$f(x,y)=\\Bigg\\{ \\begin{matrix} \\dfrac{x^2+xy^2-y}{x^2+y^2} & hvis\\ (x,y)\\neq(0,0) \\\\ 0 & hvis\\ (x,y)=(0,0) \\end{matrix}$

\n
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Punktet $(0,0)$ er et isolert punkt av $\\{(0,0)\\}\\cup\\{(x,y)|x\\geq5, y\\geq5\\}$

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Velg en riktig påstand 

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La $f:\\mathbb{R}^3\\rightarrow \\mathbb{R}^2$

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Velg hvilke funksjoner som er kontinuerlige 

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La $f:\\mathbb{R}^n\\rightarrow\\mathbb{R}^m$ og $g:\\mathbb{R}^m\\rightarrow\\mathbb{R}^p$ være kontinuerlige.

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Velg en riktig påstand

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5 minutter igjen

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