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    Complex Variables : Limits and Differentiability

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    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

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    Solution Preview

    We have:

    f'(z)= lim (f(z+deltaz)-f(z))/deltaz


    Now f(z)=1/z, therefore:

    f'(z)=lim ...

    Solution Summary

    Limits and Differentiability are investigated.