### Real Analysis

Let xn(smaller n)>=0 for all n belong to N a) if (xn)-->0, show that(sqrt[xn])-->0 b)if (xn)-->x,show that(sqrt[xn])-->x

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Let xn(smaller n)>=0 for all n belong to N a) if (xn)-->0, show that(sqrt[xn])-->0 b)if (xn)-->x,show that(sqrt[xn])-->x

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Please see the attached file for full problem description. a) Evaluate b) What is the radus of convergence .... .... To what simple function does this series converge? c) Is f(z)=... ... analytic near z= -1? and expand f(z)= ... in a power series near z= -1 can we predict the domain of convergence from the outset?

Please see the attached file for the fully formatted problems. Suppose that is not a perfect nth power, i.e K is not equal to (a) Prove that is not a member of Q, the set of all rational numbers. (b) Infer that the nth root of a natural number is either a natural number or it is irrational.

Please see the attached file for full problem description.

Antiderivative of: (t5 + 6t3) dt

See attachment

I attached a word document. Be sure to show me all of your work so that I can fully understand how to do the problems correctly. Thank you very much for your help.

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Please see the attached file for the fully formatted problem. Lim (1 - cos t)/2t t--> 0

See attached

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