Matematik Opgaver 1208 1210-1211 1216 1230


Indholdsfortegnelse

Opgave 1208

A
LaTex: F(x) = 7x+k
C
LaTex: F(x) = -\frac{1}{4}x^{-4}
H
LaTex: \begin{eqnarray} f(x) &=& (2x +4)^2\\ &=& (2x +4)\cdot (2x +4)\\ &=& 4x^2+16x+16\\ F(x) &=& \frac{4}{3}x^3+8x^2+16x+k \end{eqnarray}

Opgave 1210

LaTex: \begin{eqnarray} f(x)&=&\frac{x^2+x+1}{x+1}\\ f'(x)&=&\frac{(2x+1)\cdot(x+1)-(x^2+x+1)\cdot(1)}{(x+1)^2}\\ f'(x)&=&\frac{x^2+2x}{(x+1^2)}\\ &\Downarrow&\\ \int\frac{x^2+2x}{(x+1)^2}dx&=&\frac{x^2+x+1}{x+1}\\ f(x)&=&\frac{x^2-2x-2}{x+1}\\ f'(x)&=&\frac{(2x-2)\cdot(x+1)-(x^2-2x-2)\cdot(1)}{(x+1)^2}\\ f'(x)&=&\frac{x^2-2x-4}{(x+1)^2}\\ &\Downarrow&\\ \int\frac{x^2+2x}{(x+1)^2}dx&\neq&\frac{x^2-2x-2}{x+1}\\ \end{eqnarray} 

(%i1) solve((x^2+x+1)/(x+1)=(x^2-2*x-2)/(x+1)+k,k);
(%o1)                               [k = 3]

Opgave 1211

A
LaTex: F(x) = \frac{1}{1,5}x^{1,5}
D
LaTex: F(x) = \frac{1}{3,7}x^{3,7}
E
LaTex: F(x) = \frac{1}{2}e^{t2}-4x

Opgave 1216

LaTex: \begin{eqnarray} F(x) &=& 0,5x^2+sin(x)+4x+2 \end{eqnarray}

Opgave 1230

a
LaTex: \frac{8}{2\sqrt{1-4x}}
b
LaTex: \frac{-2(4-6x)}{12}\cdot\sqrt{2+6x}
c
LaTex: \frac{2(200-40x+12x^2)}{60}\cdot\sqrt{5+2x}
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