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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

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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.

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