1T 2011 høst LØSNING

DEL EN

a)

<tex> \frac{x^2-25}{x^2+10x+25} = \frac{(x+5)(x-5)}{(x+5)(x+5)} = \frac{x-5}{x+5}</tex>

b)

<tex> 3^{2x-1} = 1 \\ 3^{2x-1} = 3^0 \\ 2x-1 = 0 \\ x= \frac 12</tex>

c)

<tex> \frac{a^{\frac 14} \sqrt a}{(a^{\frac 34})^3 \cdot a^{-2}}= a^{\frac 14 + \frac 24 - \frac 94 + \frac 84} = a^{\frac 12} = \sqrt a </tex>

d)

<tex> A= \frac {gh}{2} \\6= \frac {5h}{2} \\ h = \frac {12}{5} </tex>

e)

Ser fra figuren at:

<tex> f(x) \leq 0 \quad \quad \quad x \in <\leftarrow,1] \cup [3, \rightarrow> \\ f(x) > g(x) \quad \quad x \in <0,5></tex>