LET X 2 An be a SEQUENCE OF COMPLEX NUMBERS THAT CONVERGES TO ZERO LIM X=0 PROVE THAT THE OPERATOR A:e e GIVEN BY n = (n. (x,",,Xz^z- FOR %3D -X,^--)is COMPACT.

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A: Prove the following limits

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A: We will find the solution of this problem.  Here,  we will use L.HOSPITAL. RULE.

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A: Solved below.