https://matematikk.net/w/api.php?action=feedcontributions&feedformat=atom&user=Matnes 2026-04-17T17:49:34Z Brukerbidrag MediaWiki 1.42.3 https://matematikk.net/w/index.php?title=R1_eksempeloppgave_2015_v%C3%A5r_L%C3%98SNING&diff=14579 2015-04-30T18:54:57Z

<p>Matnes: /* b) */</p> <hr /> <div>'''Oppgave 1'''<br /> ===a)===<br /> $f(t)=0.02t^3+0.6t^2+4.1\\f'(t)=0.06t^2+1.2t$<br /> <br /> ===b)===<br /> $g(x)=x^2\cdot \ e^{2x}\\g'(x)=2x\cdot \ e^{2x}+x^2\cdot \ 2e^{2x}=2x\cdot \ e^{2x} (1+x)$<br /> <br /> ===c)===<br /> $h(x)=ln(x^3+1)\\h'(x)=(ln u)'\cdot \ (x^3+1)' \ = \frac{1}{x^3+1}\cdot \ 3x^2 \ =\frac{3x^2}{x^3+1}$<br /> <br /> '''Opgave 2'''<br /> <br /> ===a)=== <br /> $f(x)=x^3+ax^2-13x+15$. Hvis $f(x)$ er delelig med $(x-1)$, er $f(1)=0 \\ $ $1^3+a\cdot \ 1^2-13 \cdot \ 1 +15=0 \\ 1+a+2=0 \\ a=-3$<br /> <br /> ===b)===<br /> $ \quad(x^3-3x^2-13x+15):(x-1)=x^2-2x-15\\-(x^3-x^2) \\ \quad \quad -2x^2-13x \\ \quad \quad -(-2x^2+2x) \\ \quad \quad \quad \quad -15x+15 $ <br /> <br /> <br /> Faktoriserer $x^2-2x-15$ ved abc-formelen. Da får vi at $x=5 \vee x=-3$<br /> <br /> <br /> <br /> $f(x)$ kan da skrives som $(x+3)(x-1)(x-5)$ , hvor alle ledd er av første grad.</div>

Matnes https://matematikk.net/w/index.php?title=R1_eksempeloppgave_2015_v%C3%A5r_L%C3%98SNING&diff=14578 2015-04-30T18:41:24Z

<p>Matnes: /* b) */</p> <hr /> <div>'''Oppgave 1'''<br /> ===a)===<br /> $f(t)=0.02t^3+0.6t^2+4.1\\f'(t)=0.06t^2+1.2t$<br /> <br /> ===b)===<br /> $g(x)=x^2\cdot \ e^{2x}\\g'(x)=2x\cdot \ e^{2x}+x^2\cdot \ 2e^{2x}=2x\cdot \ e^{2x} (1+x)$<br /> <br /> ===c)===<br /> $h(x)=ln(x^3+1)\\h'(x)=(ln u)'\cdot \ (x^3+1)' \ = \frac{1}{x^3+1}\cdot \ 3x^2 \ =\frac{3x^2}{x^3+1}$<br /> <br /> '''Opgave 2'''<br /> <br /> ===a)=== <br /> $f(x)=x^3+ax^2-13x+15$. Hvis $f(x)$ er delelig med $(x-1)$, er $f(1)=0 \\ $ $1^3+a\cdot \ 1^2-13 \cdot \ 1 +15=0 \\ 1+a+2=0 \\ a=-3$<br /> <br /> ===b)===<br /> $ \quad(x^3-3x^2-13x+15):(x-1)=x^2-2x-15\\-(x^3-x^2) \\ \quad \quad -2x^2-13x \\ \quad \quad -(-2x^2+2x) \\ \quad \quad \quad \quad -15x+15 $</div>

Matnes https://matematikk.net/w/index.php?title=R1_eksempeloppgave_2015_v%C3%A5r_L%C3%98SNING&diff=14577 2015-04-30T18:34:25Z

<p>Matnes: /* a) */</p> <hr /> <div>'''Oppgave 1'''<br /> ===a)===<br /> $f(t)=0.02t^3+0.6t^2+4.1\\f'(t)=0.06t^2+1.2t$<br /> <br /> ===b)===<br /> $g(x)=x^2\cdot \ e^{2x}\\g'(x)=2x\cdot \ e^{2x}+x^2\cdot \ 2e^{2x}=2x\cdot \ e^{2x} (1+x)$<br /> <br /> ===c)===<br /> $h(x)=ln(x^3+1)\\h'(x)=(ln u)'\cdot \ (x^3+1)' \ = \frac{1}{x^3+1}\cdot \ 3x^2 \ =\frac{3x^2}{x^3+1}$<br /> <br /> '''Opgave 2'''<br /> <br /> ===a)=== <br /> $f(x)=x^3+ax^2-13x+15$. Hvis $f(x)$ er delelig med $(x-1)$, er $f(1)=0 \\ $ $1^3+a\cdot \ 1^2-13 \cdot \ 1 +15=0 \\ 1+a+2=0 \\ a=-3$<br /> <br /> ===b)===<br /> $ \quad(x^3-3x^2-13x+15):(x-1)=x^2-2x-15\\-(x^3-x^2)\\ quad \quad \-2x^2-13x \\quad \quad \quad \quad \-2x^2+2x$</div>

Matnes https://matematikk.net/w/index.php?title=R1_eksempeloppgave_2015_v%C3%A5r_L%C3%98SNING&diff=14576 2015-04-30T14:56:37Z

<p>Matnes: /* a) */</p> <hr /> <div>'''Oppgave 1'''<br /> ===a)===<br /> $f(t)=0.02t^3+0.6t^2+4.1\\f'(t)=0.06t^2+1.2t$<br /> <br /> ===b)===<br /> $g(x)=x^2\cdot \ e^{2x}\\g'(x)=2x\cdot \ e^{2x}+x^2\cdot \ 2e^{2x}=2x\cdot \ e^{2x} (1+x)$<br /> <br /> ===c)===<br /> $h(x)=ln(x^3+1)\\h'(x)=(ln u)'\cdot \ (x^3+1)' \ = \frac{1}{x^3+1}\cdot \ 3x^2 \ =\frac{3x^2}{x^3+1}$<br /> <br /> '''Opgave 2'''<br /> <br /> ===a)=== <br /> $f(x)=x^3+ax^2-13x+15$. Hvis $f(x)$ er delelig med $(x-1)$, er $f(1)=0 \\ $ $1^3+a\cdot \ 1^2-13 \cdot \ 1 +15=0 \\ 1+a+2=0 \\ a=-3$</div>

Matnes https://matematikk.net/w/index.php?title=R1_eksempeloppgave_2015_v%C3%A5r_L%C3%98SNING&diff=14575 2015-04-30T14:55:36Z

<p>Matnes: /* a) */</p> <hr /> <div>'''Oppgave 1'''<br /> ===a)===<br /> $f(t)=0.02t^3+0.6t^2+4.1\\f'(t)=0.06t^2+1.2t$<br /> <br /> ===b)===<br /> $g(x)=x^2\cdot \ e^{2x}\\g'(x)=2x\cdot \ e^{2x}+x^2\cdot \ 2e^{2x}=2x\cdot \ e^{2x} (1+x)$<br /> <br /> ===c)===<br /> $h(x)=ln(x^3+1)\\h'(x)=(ln u)'\cdot \ (x^3+1)' \ = \frac{1}{x^3+1}\cdot \ 3x^2 \ =\frac{3x^2}{x^3+1}$<br /> <br /> '''Opgave 2'''<br /> <br /> ===a)=== <br /> $f(x)=x^3+ax^2-13x+15$. Hvis $f(x)$ er delelig med $(x-1)$, er $f(1)=0 \\ $ $1^3+a\cdot \ 1^2-13 \cdot \ 1 -15=0 \\ 1+a+2=0 \\ a=-3$</div>

Matnes https://matematikk.net/w/index.php?title=R1_eksempeloppgave_2015_v%C3%A5r_L%C3%98SNING&diff=14574 2015-04-30T14:55:19Z

<p>Matnes: /* a) */</p> <hr /> <div>'''Oppgave 1'''<br /> ===a)===<br /> $f(t)=0.02t^3+0.6t^2+4.1\\f'(t)=0.06t^2+1.2t$<br /> <br /> ===b)===<br /> $g(x)=x^2\cdot \ e^{2x}\\g'(x)=2x\cdot \ e^{2x}+x^2\cdot \ 2e^{2x}=2x\cdot \ e^{2x} (1+x)$<br /> <br /> ===c)===<br /> $h(x)=ln(x^3+1)\\h'(x)=(ln u)'\cdot \ (x^3+1)' \ = \frac{1}{x^3+1}\cdot \ 3x^2 \ =\frac{3x^2}{x^3+1}$<br /> <br /> '''Opgave 2'''<br /> <br /> ===a)=== <br /> $f(x)=x^3+ax^2-13x+15$. Hvis $f(x)$ er delelig med $(x-1)$, er $f(1)=0 \\ $ $1^3+a\cdot \ 1^2-13 \cdot \ 1 -15=0 \\ 1+a+2=0 \\ a=3$</div>

Matnes https://matematikk.net/w/index.php?title=R1_eksempeloppgave_2015_v%C3%A5r_L%C3%98SNING&diff=14573 2015-04-30T14:53:59Z

<p>Matnes: /* a) */</p> <hr /> <div>'''Oppgave 1'''<br /> ===a)===<br /> $f(t)=0.02t^3+0.6t^2+4.1\\f'(t)=0.06t^2+1.2t$<br /> <br /> ===b)===<br /> $g(x)=x^2\cdot \ e^{2x}\\g'(x)=2x\cdot \ e^{2x}+x^2\cdot \ 2e^{2x}=2x\cdot \ e^{2x} (1+x)$<br /> <br /> ===c)===<br /> $h(x)=ln(x^3+1)\\h'(x)=(ln u)'\cdot \ (x^3+1)' \ = \frac{1}{x^3+1}\cdot \ 3x^2 \ =\frac{3x^2}{x^3+1}$<br /> <br /> '''Opgave 2'''<br /> <br /> ===a)=== <br /> $f(x)=x^3+ax^2-13x+15$. Hvis $f(x)$ er delelig med $(x-1)$, er $f(1)=0 \\ $ $1^3+a\cdot \ 1^2-13 \cdot \ 1 -15=0 \ 1+a+2=0 \ a=3$</div>

Matnes https://matematikk.net/w/index.php?title=R1_eksempeloppgave_2015_v%C3%A5r_L%C3%98SNING&diff=14572 2015-04-30T14:53:03Z

<p>Matnes: /* a) */</p> <hr /> <div>'''Oppgave 1'''<br /> ===a)===<br /> $f(t)=0.02t^3+0.6t^2+4.1\\f'(t)=0.06t^2+1.2t$<br /> <br /> ===b)===<br /> $g(x)=x^2\cdot \ e^{2x}\\g'(x)=2x\cdot \ e^{2x}+x^2\cdot \ 2e^{2x}=2x\cdot \ e^{2x} (1+x)$<br /> <br /> ===c)===<br /> $h(x)=ln(x^3+1)\\h'(x)=(ln u)'\cdot \ (x^3+1)' \ = \frac{1}{x^3+1}\cdot \ 3x^2 \ =\frac{3x^2}{x^3+1}$<br /> <br /> '''Opgave 2'''<br /> <br /> ===a)=== <br /> $f(x)=x^3+ax^2-13x+15$. Hvis $f(x)$ er delelig med $(x-1)$, er $f(1)=0 \\ $1^3+a\cdot \ 1^2-13 \cdot \ 1 -15=0 \ 1+a+2=0 \ a=3$</div>

Matnes https://matematikk.net/w/index.php?title=R1_eksempeloppgave_2015_v%C3%A5r_L%C3%98SNING&diff=14571 2015-04-30T14:52:41Z

<p>Matnes: /* a) */</p> <hr /> <div>'''Oppgave 1'''<br /> ===a)===<br /> $f(t)=0.02t^3+0.6t^2+4.1\\f'(t)=0.06t^2+1.2t$<br /> <br /> ===b)===<br /> $g(x)=x^2\cdot \ e^{2x}\\g'(x)=2x\cdot \ e^{2x}+x^2\cdot \ 2e^{2x}=2x\cdot \ e^{2x} (1+x)$<br /> <br /> ===c)===<br /> $h(x)=ln(x^3+1)\\h'(x)=(ln u)'\cdot \ (x^3+1)' \ = \frac{1}{x^3+1}\cdot \ 3x^2 \ =\frac{3x^2}{x^3+1}$<br /> <br /> '''Opgave 2'''<br /> <br /> ===a)=== <br /> $f(x)=x^3+ax^2-13x+15$. Hvis $f(x)$ er delelig med $(x-1)$, er $f(1)=0\\<br /> $1^3+a\cdot \ 1^2-13 \cdot \ 1 -15=0 \ 1+a+2=0 \ a=3$</div>

Matnes https://matematikk.net/w/index.php?title=R1_eksempeloppgave_2015_v%C3%A5r_L%C3%98SNING&diff=14570 2015-04-30T14:51:50Z

<p>Matnes: /* c) */</p> <hr /> <div>'''Oppgave 1'''<br /> ===a)===<br /> $f(t)=0.02t^3+0.6t^2+4.1\\f'(t)=0.06t^2+1.2t$<br /> <br /> ===b)===<br /> $g(x)=x^2\cdot \ e^{2x}\\g'(x)=2x\cdot \ e^{2x}+x^2\cdot \ 2e^{2x}=2x\cdot \ e^{2x} (1+x)$<br /> <br /> ===c)===<br /> $h(x)=ln(x^3+1)\\h'(x)=(ln u)'\cdot \ (x^3+1)' \ = \frac{1}{x^3+1}\cdot \ 3x^2 \ =\frac{3x^2}{x^3+1}$<br /> <br /> '''Opgave 2'''<br /> <br /> ===a)=== <br /> $f(x)=x^3+ax^2-13x+15$. Hvis $f(x)$ er delelig med $(x-1)$, er $f(1)=0<br /> $1^3+a\cdot \ 1^2-13 \cdot \ 1 -15=0 \ 1+a+2=0 \ a=3$</div>

Matnes https://matematikk.net/w/index.php?title=R1_eksempeloppgave_2015_v%C3%A5r_L%C3%98SNING&diff=14569 2015-04-30T14:44:08Z

<p>Matnes: /* c) */</p> <hr /> <div>'''Oppgave 1'''<br /> ===a)===<br /> $f(t)=0.02t^3+0.6t^2+4.1\\f'(t)=0.06t^2+1.2t$<br /> <br /> ===b)===<br /> $g(x)=x^2\cdot \ e^{2x}\\g'(x)=2x\cdot \ e^{2x}+x^2\cdot \ 2e^{2x}=2x\cdot \ e^{2x} (1+x)$<br /> <br /> ===c)===<br /> $h(x)=ln(x^3+1)\\h'(x)=(ln u)'\cdot \ (x^3+1)' \ = \frac{1}{x^3+1}\cdot \ 3x^2 \ =\frac{3x^2}{x^3+1}$</div>

Matnes https://matematikk.net/w/index.php?title=R1_eksempeloppgave_2015_v%C3%A5r_L%C3%98SNING&diff=14568 2015-04-30T14:43:55Z

<p>Matnes: /* c) */</p> <hr /> <div>'''Oppgave 1'''<br /> ===a)===<br /> $f(t)=0.02t^3+0.6t^2+4.1\\f'(t)=0.06t^2+1.2t$<br /> <br /> ===b)===<br /> $g(x)=x^2\cdot \ e^{2x}\\g'(x)=2x\cdot \ e^{2x}+x^2\cdot \ 2e^{2x}=2x\cdot \ e^{2x} (1+x)$<br /> <br /> ===c)===<br /> $h(x)=ln(x^3+1)\\h'(x)=(lnu)'\cdot \ (x^3+1)' \ = \frac{1}{x^3+1}\cdot \ 3x^2 \ =\frac{3x^2}{x^3+1}$</div>

Matnes https://matematikk.net/w/index.php?title=R1_eksempeloppgave_2015_v%C3%A5r_L%C3%98SNING&diff=14567 2015-04-30T14:43:36Z

<p>Matnes: /* c) */</p> <hr /> <div>'''Oppgave 1'''<br /> ===a)===<br /> $f(t)=0.02t^3+0.6t^2+4.1\\f'(t)=0.06t^2+1.2t$<br /> <br /> ===b)===<br /> $g(x)=x^2\cdot \ e^{2x}\\g'(x)=2x\cdot \ e^{2x}+x^2\cdot \ 2e^{2x}=2x\cdot \ e^{2x} (1+x)$<br /> <br /> ===c)===<br /> $h(x)=ln(x^3+1)\\h'(x)=(lnu)'\cdot \ (x^3+1)' \= \frac{1}{x^3+1}\cdot \ 3x^2 \=\frac{3x^2}{x^3+1}$</div>

Matnes https://matematikk.net/w/index.php?title=R1_eksempeloppgave_2015_v%C3%A5r_L%C3%98SNING&diff=14566 2015-04-30T14:42:59Z

<p>Matnes: /* c) */</p> <hr /> <div>'''Oppgave 1'''<br /> ===a)===<br /> $f(t)=0.02t^3+0.6t^2+4.1\\f'(t)=0.06t^2+1.2t$<br /> <br /> ===b)===<br /> $g(x)=x^2\cdot \ e^{2x}\\g'(x)=2x\cdot \ e^{2x}+x^2\cdot \ 2e^{2x}=2x\cdot \ e^{2x} (1+x)$<br /> <br /> ===c)===<br /> $h(x)=ln(x^3+1)\\h'(x)=(lnu)'\cdot \ (x^3+1)'&amp;=&amp; \frac{1}{x^3+1}\cdot \ 3x^2 &amp;=&amp;\frac{3x^2}{x^3+1}$</div>

Matnes https://matematikk.net/w/index.php?title=R1_eksempeloppgave_2015_v%C3%A5r_L%C3%98SNING&diff=14565 2015-04-30T14:42:20Z

<p>Matnes: /* c) */</p> <hr /> <div>'''Oppgave 1'''<br /> ===a)===<br /> $f(t)=0.02t^3+0.6t^2+4.1\\f'(t)=0.06t^2+1.2t$<br /> <br /> ===b)===<br /> $g(x)=x^2\cdot \ e^{2x}\\g'(x)=2x\cdot \ e^{2x}+x^2\cdot \ 2e^{2x}=2x\cdot \ e^{2x} (1+x)$<br /> <br /> ===c)===<br /> $h(x)=ln(x^3+1)\\h'(x)=(lnu)'\cdot \ (x^3+1)'\\= \frac{1}{x^3+1}\cdot \ 3x^2\\=\frac{3x^2}{x^3+1}$</div>

Matnes https://matematikk.net/w/index.php?title=R1_eksempeloppgave_2015_v%C3%A5r_L%C3%98SNING&diff=14564 2015-04-30T14:42:07Z

<p>Matnes: /* c) */</p> <hr /> <div>'''Oppgave 1'''<br /> ===a)===<br /> $f(t)=0.02t^3+0.6t^2+4.1\\f'(t)=0.06t^2+1.2t$<br /> <br /> ===b)===<br /> $g(x)=x^2\cdot \ e^{2x}\\g'(x)=2x\cdot \ e^{2x}+x^2\cdot \ 2e^{2x}=2x\cdot \ e^{2x} (1+x)$<br /> <br /> ===c)===<br /> $h(x)=ln(x^3+1)\\h'(x)=(lnu)'\cdot \ (x^3+1)'\\= \frac{1}{x^3+1}\cdot \ 3x^2\\=\frac{3x^2}{x^3+1}</div>

Matnes https://matematikk.net/w/index.php?title=R1_eksempeloppgave_2015_v%C3%A5r_L%C3%98SNING&diff=14563 2015-04-30T14:41:29Z

<p>Matnes: /* b) */</p> <hr /> <div>'''Oppgave 1'''<br /> ===a)===<br /> $f(t)=0.02t^3+0.6t^2+4.1\\f'(t)=0.06t^2+1.2t$<br /> <br /> ===b)===<br /> $g(x)=x^2\cdot \ e^{2x}\\g'(x)=2x\cdot \ e^{2x}+x^2\cdot \ 2e^{2x}=2x\cdot \ e^{2x} (1+x)$<br /> <br /> ===c)===<br /> $h(x)=ln(x^3+1)\\h'(x)=(lnu)'\cdot \ (x^3+1)' &amp;=&amp;\frac{1}{x^3+1}\cdot \ 3x^2 &amp;=&amp; \frac{3x^2}{x^3+1}</div>

Matnes https://matematikk.net/w/index.php?title=R1_eksempeloppgave_2015_v%C3%A5r_L%C3%98SNING&diff=14562 2015-04-30T14:31:05Z

<p>Matnes: /* b) */</p> <hr /> <div>'''Oppgave 1'''<br /> ===a)===<br /> $f(t)=0.02t^3+0.6t^2+4.1\\f'(t)=0.06t^2+1.2t$<br /> <br /> ===b)===<br /> $g(x)=x^2\cdot \ e^{2x}\\g'(x)=2x\cdot \ e^{2x}+x^2\cdot \ 2e^{2x}=2x\cdot \ e^{2x} (1+x)$</div>

Matnes https://matematikk.net/w/index.php?title=R1_eksempeloppgave_2015_v%C3%A5r_L%C3%98SNING&diff=14561 2015-04-30T14:30:28Z

<p>Matnes: /* b) */</p> <hr /> <div>'''Oppgave 1'''<br /> ===a)===<br /> $f(t)=0.02t^3+0.6t^2+4.1\\f'(t)=0.06t^2+1.2t$<br /> <br /> ===b)===<br /> $g(x)=x^2\cdot \ e^{2x}\\g'(x)=2x\cdot \ e^{2x}+x^2\cdot \ 2e^{2x}=2x e^{2x} (1+x)$</div>

Matnes https://matematikk.net/w/index.php?title=R1_eksempeloppgave_2015_v%C3%A5r_L%C3%98SNING&diff=14560 2015-04-30T14:26:04Z

<p>Matnes: /* b) */</p> <hr /> <div>'''Oppgave 1'''<br /> ===a)===<br /> $f(t)=0.02t^3+0.6t^2+4.1\\f'(t)=0.06t^2+1.2t$<br /> <br /> ===b)===<br /> $g(x)=x^2\cdot \ e^{2x}\\g'(x)=2x\cdot \ e^{2x}+x^2\cdot \ 2e^{2x}=2x\cdot \ e^{2x}\cdot \ (1+x)$</div>

Matnes https://matematikk.net/w/index.php?title=R1_eksempeloppgave_2015_v%C3%A5r_L%C3%98SNING&diff=14559 2015-04-30T14:25:29Z

<p>Matnes: /* b) */</p> <hr /> <div>'''Oppgave 1'''<br /> ===a)===<br /> $f(t)=0.02t^3+0.6t^2+4.1\\f'(t)=0.06t^2+1.2t$<br /> <br /> ===b)===<br /> $g(x)=x^2\cdot \e^{2x}\\g'(x)=2x\cdot \e^{2x}+x^2\cdot \2e^{2x}=2x\cdot \e^{2x}\cdot \(1+x)$</div>

Matnes https://matematikk.net/w/index.php?title=R1_eksempeloppgave_2015_v%C3%A5r_L%C3%98SNING&diff=14558 2015-04-30T14:24:00Z

<p>Matnes: /* a) */</p> <hr /> <div>'''Oppgave 1'''<br /> ===a)===<br /> $f(t)=0.02t^3+0.6t^2+4.1\\f'(t)=0.06t^2+1.2t$<br /> <br /> ===b)===<br /> $g(x)=x^2\cdot\e^{2x}\\g'(x)=2x\cdot\e^{2x}+x^2\cdot\2e^{2x}=2x\cdot\e^{2x}\cdot\(1+x)$</div>

Matnes https://matematikk.net/w/index.php?title=R1_eksempeloppgave_2015_v%C3%A5r_L%C3%98SNING&diff=14557 2015-04-30T13:53:50Z

<p>Matnes: /* a) */</p> <hr /> <div>'''Oppgave 1'''<br /> ===a)===<br /> $f(t)=0.02t^3+0.6t^2+4.1\\f'(t)=0.06t^2+1.2t$</div>

Matnes https://matematikk.net/w/index.php?title=R1_eksempeloppgave_2015_v%C3%A5r_L%C3%98SNING&diff=14556 2015-04-30T13:52:48Z

<p>Matnes: Ny side: &#039;&#039;&#039;Oppgave 1&#039;&#039;&#039; ===a)=== $f(t)=0.02t^3+0.06t^2+4.1\\f&#039;(t)=0.06t^2+1.2t$</p> <hr /> <div>'''Oppgave 1'''<br /> ===a)===<br /> $f(t)=0.02t^3+0.06t^2+4.1\\f'(t)=0.06t^2+1.2t$</div>

Matnes