1. What is the difference between the Riemann integral and the
Darboux Integral?
2. Give the same characteristics between Riemann integrals and
Darboux integrals !.
Explain the difference between the actual definition of a
Riemann Integral of function f on the interval [a,b] and the
conclusion of the FTOC Part 2.(Fundamental Theorem of Calculus Part
2)
Explain the difference between the actual definition of a
Riemann Integral of function f on the interval [a,b] and the
conclusion of the FTOC Part 2.(Fundamental Theorem of Calculus Part
2)
What are the different methods used to show a function is equal
to its Taylor series near its center. In particular discuss
Taylor’s inequality and how it can be used. Give a detailed
example.
17. Integrate the function sin(x) from 0 to π using Riemann and
Simpson integration methods with N subintervals, where N increases
by factors of 2 from 2 to 256 (i.e. N = 2, N = 4, etc.). Plot the
relative error ∆I/I = [| estimated value - true value |/(true
value)], assuming the
highest value of N gives the ‘true’ value. Which method
converges the fastest?