DEL 1

Oppgave 1

$f (x) = 4 x^{2} \cdot l n (3 x)$

$f^{'} (x) = 8 x \cdot l n (3 x) + 4 x^{2} \cdot \frac{1}{3 x} \cdot 3$

$f^{'} (x) = 8 x \cdot l n (3 x) + 4 x$

$(l n x)^{2} - l n x = 6$

Setter $u = l n x$

$u^{2} - u - 6 = 0$

$(u + 2) (u - 3) = 0$

$u = - 2 \lor u = 3$

$l n x = - 2 \lor l n x = 3$

$x = e^{- 2} \lor x = e^{3}$

$x = \frac{1}{e^{2}} \lor x = e^{3}$

$f (x) = e^{- x + 1}, D_{f} = R$

$lim_{x \to \infty} e^{- x + 1} = e^{- \infty} = \frac{1}{e^{\infty}} = 0$

$lim_{x \to - \infty} e^{- x + 1} = e^{\infty} = \infty$

P(2 gule sokker) = $P (G) \cdot P (G | G) = \frac{6}{15} \cdot \frac{5}{14} = \frac{30}{15 \cdot 14} = \frac{2}{14} = \frac{1}{7}$