The lim of x approaches 0 for ((3+x)^-1 - 3^-1)/x. So I tried to first switch the numerator to the bottom to get rid of the neg exponents. I got stuck and couldn't solve the damn thing. I then multiply by the conjugate up to this point:
(x(x+x)+3))/(x+x)^2 - 9)
Anyway, I've been staring at this thing for a while, ama throw the towel. Thanks.
(x(x+x)+3))/(x+x)^2 - 9)
Anyway, I've been staring at this thing for a while, ama throw the towel. Thanks.
-
((3+x)^-1 - 3^-1)/x = (1/(3 + x) - 1/3)/x
= (3 - (3 + x))/(3(3 + x))/x
= -1/(3(3 + x))
Lim x->0 ((3+x)^-1 - 3^-1)/x = - Lim x->0 1/(3(3 + x)) = -1/9
= (3 - (3 + x))/(3(3 + x))/x
= -1/(3(3 + x))
Lim x->0 ((3+x)^-1 - 3^-1)/x = - Lim x->0 1/(3(3 + x)) = -1/9