Obligatoriske oppgaver for uke 3
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\n\nNB: I denne oppgaven må du være obs på syntax. Hvis du f.eks. trenger å skrive inn $3x^2\\sin^2 x^5$ skriver du: 3x^2*(sin(x^5))^2 (IKKE 3x^2*(sin^2(x^5)))
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\n$\\frac{\\partial f}{\\partial x}$ = [[0]]
\n$\\frac{\\partial f}{\\partial y}$ = [[1]]
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\n\nVær obs på skrivemåten: f.eks, hvis du trenger å skrive inn $3x^2 e^y-\\ln x$ skriver du: 3x^2*e^y-ln(x) (IKKE 3x^2e^y-lnx). I NUMBAS er det tryggest å skrive alle multiplikasjonstegnene.
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\n$\\frac{\\partial f}{\\partial x}$ = [[0]]
\n$\\frac{\\partial f}{\\partial y}$ = [[1]]
\n$\\frac{\\partial^2 f}{\\partial x^2}$ = [[2]]
\n$\\frac{\\partial^2 f}{\\partial y^2}$ = [[3]]
\n$\\frac{\\partial^2 f}{\\partial x \\partial y}$ =[[4]]
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", "advice": "Eksistensen av de partiellderiverte $f_x(a,b)$ og $f_y(a,b)$ er ikke tilstrekkelig til å garantere at grafen har et tangentplan i $(a, b, f(a,b))$
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\nPåstand:
\nI punktet $(a,b)$ har da $f$ et tangentplan gitt ved
\n$z=f(a,b)+f_x(a,b)(x-a)+f_y(a,b)(y-b)$
\nEr denne påstanden sann eller usann?
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\n$z=$ [[0]] + [[1]] $(x-(\\var{f}))$+ [[2]] $(y-\\var{g})$
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