Complex analysis by Joseph Bak and Donald untal Tine šegments). 6. Prove that if

Question

Complex analysis by Joseph Bak and Donald
untal Tine šegments). 6. Prove that if E is connected and if f : E C is continuous, then f(E) is connected. 7. Let {an}ool be a sequence of real numbers, and let lim sup an:lim (supfan, an+1, an+2,...]). 8. Prove that lim supn too an-L e R if and only if the following two conditions hold true: (1) For every e0 there exists an index N such that an SL+e for all n > N; (9) For each e 0 and for each index N, there exists some na > N such that an L-. 9. Let 000CkZk be a power series, and let R := E lo, ool. 29 lim sup VIckl Prove that the series converges uniformly and absolutely on any closed disk |al S r with r R. 10. Let (2nl n be a sequence of complex numbers converging to the complex number z. Prove that 21+Zn

Explanation / Answer

question 7 is a definition of limit superior, it is not asking us anything to prove there, it is just a definition please kindly clearly ask the question. becuase the definitions are trivial.

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