1) It shows that the function f(x) = 1/x is integrable in the closed interval [1, 2]. This must be done estimating the Riemann sums of the function f(x).
1) It shows that the function f(x) = 1/x is integrable in the closed interval [1, 2]. This must be done estimating the Riemann sums of the function f(x).
2)Propose a limited function f : [a, b] → R and two P and Q partitions of the closed interval [a, b] such
that λ(P) < λ(Q) but that lower sum (f; P) = lower sum(f; Q) and superior sum (f; P) = superior sum(f; Q).
3)Let f : [a, b] → R a continuous function such that f(x) ≥ 0 for all x ∈ [a, b]. It proves that if there is
x0 ∈ (a, b) such that f(x0)>0, then:
The
Note: do not demonstrate 3) with a numerical example
4)Give an example of a dimensioned function f : [a, b] → R such that |f| is Riemann-integratable, but f not
is Riemann-integrable.
5)Build two examples of functions f1,2 : [a, b] → R that are Riemann-integratable where
1/f1(X)
is not Riemann-integrable and 1/f2(X)
if Riemann-integrable
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