-
contains X. An
interval I is a
subinterval of
interval J if I is a
subset of J. An
interval I is a
proper subinterval of J if I is a
proper subset of...
- best
approached with
subintervals of
equal size. The
interval [a, b] is
therefore divided into n {\displaystyle n}
subintervals, each of
length Δ x =...
- distributed, if the
proportion of
terms falling in a
subinterval is
proportional to the
length of that
subinterval. Such
sequences are
studied in
Diophantine approximation...
- two
equally sized subintervals.
Because each
sequence has
infinitely many members,
there must be (at least) one of
these subintervals that
contains infinitely...
- [a,b]} into n > 2 {\displaystyle n>2}
small subintervals. Simpson's rule is then
applied to each
subinterval, with the
results being summed to
produce an...
- on each
subinterval. (When f is
discontinuous on a
subinterval,
there may not be a tag that
achieves the
infimum or
supremum on that
subinterval.) The Darboux...
-
partitioning the
integration interval,
applying the
trapezoidal rule to each
subinterval, and
summing the results. In practice, this "chained" (or "composite")...
-
replacing these subintervals by ones with the left end
height of each piece, the
approximation one gets is too low: with
twelve such
subintervals the approximated...
-
whose heights are the
supremum and infimum, respectively, of f in each
subinterval of the partition.
These ideas are made
precise below: A
partition of...
-
point of I.
Every interval of the form [xi, xi + 1] is
referred to as a
subinterval of the
partition x.
Another partition Q of the
given interval [a, b]...
