Grenseverdi

[tarjei]

finn lim x-->3 for
5x-15
[symbol:rot] (x+1) -2




kvadratroten er av verdien x+1

[ingentingg]

[tex]\lim_{x\to 3} \frac{5x-15}{\sqrt{x+1} -2} = \lim_{x\to 3} \frac{(5x-15)(\sqrt{x+1}+2)}{(\sqrt{x+1} -2)(\sqrt{x+1}+2)} = \lim_{x\to 3} \frac{5(x-3)(\sqrt{x+1}+2)}{(x+1-4)} = \\ \lim_{x\to 3} \frac{5(x-3)(\sqrt{x+1}+2)}{(x-3)} = \lim_{x\to 3} 5 (\sqrt{x+1}+2) = 5(\sqrt{4}+2) = 20[/tex]