Questions asked by Entertainment U.

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• How to prove that (tan b / tab a) > (b/a) whenever 0 < a < b < π/2?
  
• How to calculate present value?
  
• Is #sum_"n=1"^infty 3^(1 - n) * 5^(n/2)# convergent or divergent? if it's convergent, find its sum.
  
• How is -ln |cos x| = ln (1/|cos x|) ?
  
• How to show that #1/(2a) ln |(x - a)/(x + a)| + C# is equal to #1/(2a) ln |(x + a)/(x - a)| + K#?
  
• How to evaluate #int dx/(a sin x + b cos x)# where #b > 0#?