Complex Variables : Limits and Differentiability
3. Give a direct proof that
f ΄(z) = -1 / z2 when f (z) = 1 / z (z ≠0).
Use this definition to prove the problem.
dw / dz = lim ∆w / ∆z
∆z→0
https://brainmass.com/math/complex-analysis/complex-variables-limits-differentiability-33011
Solution Preview
We have:
f'(z)= lim (f(z+deltaz)-f(z))/deltaz
deltaz--->0
Now f(z)=1/z, therefore:
f'(z)=lim ...
Solution Summary
Limits and Differentiability are investigated.
$2.19