form. def. på en grenseverdi
Lagt inn: 22/05-2005 16:13
lim (x[sup]2[/sup] + 3x +2)/(x-1) = 12
x-->2
|(x[sup]2[/sup] + 3x +2)/(x-1) - 12| < epsilon
==> |(x[sup]2[/sup] - 9x + 14)/(x-1)| < epsilon
==> |((x-2)*(x-7))/(x-1)| < epsilon
==> |x-2| < epsilon*(x-1)/(x-7)
0 < |x-2| < delta
|x-2| < delta = epsilon*(x-1)/(x-7)
==> ((x-2)(x-7))/(x-1) < epsilon
Gjør jeg noe feil her ?
x-->2
|(x[sup]2[/sup] + 3x +2)/(x-1) - 12| < epsilon
==> |(x[sup]2[/sup] - 9x + 14)/(x-1)| < epsilon
==> |((x-2)*(x-7))/(x-1)| < epsilon
==> |x-2| < epsilon*(x-1)/(x-7)
0 < |x-2| < delta
|x-2| < delta = epsilon*(x-1)/(x-7)
==> ((x-2)(x-7))/(x-1) < epsilon
Gjør jeg noe feil her ?
