Questions asked by Babette

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• What is #lim_(x=>0^+)x^(1/x)# ?
  
• How do you determine if the following integral is convergent or divergent using the comparison theorem? #int_0^oo (arctan(x))/(2+e^x)dx#
  
• Find the radius of convergence of the following series. Does it converge or diverge? #sum_(n=1)^oo((-1)^nx^n)/root(9)(n)#