We have that for the Question "Find the minimum value of n that guarantees an error of no more than 1/30,000 in approximating integral 1/x dx from 3 to 4 by the Trapezoidal Rule with n equal sub intervals" it can be said that the minimum value of n that guarantees an error of no more than 1/30,000 is
\(n \geq 9\)
From the question we are told
Find the minimum value of n that guarantees an error of no more than 1/30,000 in approximating integral 1/x dx from 3 to 4 by the Trapezoidal Rule with n equal sub intervals
Generally the equation for the minimum value is mathematically given as
\(E=\frac{K(b-a^3)}{12n^2}\\\\Here\\\\f''(x) \leq K\)
Therefore
\(f(x)=\frac{1}{x}\\\\f''(x)=\frac{2}{x^3}\\\\|\frac{2}{x^3}|= 1/32\\\\\)
Therefore
\(E=\frac{1/32*1^3}{12n^2}\\\\\frac{1/32*1^3}{12n^2}=\frac{1}{30000}\\\\\)
\(n \geq 9\)
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