2.5.3 Can you answer these questions?

2.5.3.1 How to add AccuracyGoal and PrecisionGoal options in a numerical function?

http://mathematica.stackexchange.com/questions/88182/how-to-add-accuracygoal-and-precisiongoal-options-in-a-numerical-function

 
There are many built-in functions that contain AccuracyGoal, PrecisionGoal and WorkingPrecision. 
 
 
 
 
 
For instance 
 
NSolve 
 
NSolve[x^3 + 2 x + 7 == 0, x, WorkingPrecision -> 40] 
 
 
 
{{x ->  ...
 

- asked by Shutao Tang 4votes

2.5.3.2 What is the best way to take the Bourdet derivative?

http://mathematica.stackexchange.com/questions/87760/what-is-the-best-way-to-take-the-bourdet-derivative

 
Given a list of paired delta-time, delta-pressure, $(dt,dp)$, what might be the best approach to calculate the Bourdet derivative, described below?  I am unclear how to manipulate elements of the  ...
 

- asked by John 4votes

2.5.3.3 Dirichlet coefficients as limits: wrong

http://mathematica.stackexchange.com/questions/87766/dirichlet-coefficients-as-limits-wrong

 
Perhaps I should have included the word "bug" in my question. Here we go 
 
There is a bug in this Limit 
 
Limit[3^s (-1 - 2^-s + Zeta[s]), s -> \[Infinity]] 
(* 0 *) 
 
 
It should be 1 
 
and there is a  ...
 

- asked by Dr. Wolfgang Hintze 7votes

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