Theorem: Suppose that
lim as z-->z0 of f(z)=w0 and
lim as z-->z0 of F(z)=W0
lim as z-->z0 of [f(z)+F(z)]=w0 + W0,
lim as z-->z0 of [f(z)F(z)]=w0*W0 and
if W0 can not equal 0, then
lim as z-->z0 of f(z)/F(z)=w0/W0.
Find lim as z--> i of ((iz^3)-1) / (z+i).© BrainMass Inc. brainmass.com March 4, 2021, 10:33 pm ad1c9bdddf
Well, if you take
f(z) = iz^3 - 1
F(z) = z + i
then lim (iz^3 - 1)/(z+i) as z goes to i is lim f(z)/F(z).
Now, if we can find the limits as z->i ...
The theorem is utilized.