Continuity and sequences - UNSA MP 2001
functions of one real variable
180 2001
3
U1
analysis, calculus
epsilon, limit, minimum, maximum, extremum, recursive sequence, convergence


This is the translation of a sheet designed for first year students of mathematics and physics at Université de Nice - Sophia Antipolis, of year 2000-2001.  Each student has had 3 hours to work on this sheet.

:U1/analysis/epsilon.en
aide=1
30
0.6
Epsilon
on the definition of continuity: given epsilon, find delta.
:U1/analysis/aplat.en
order=2&fundif=1&tolerance=0.005
10
0.7
Flatten I
parametrize a function to make it infinitesimal at a point.
:U1/analysis/aplat.en
order=2&fundif=3&tolerance=0.001
20
1
Flatten II
parametrize a function to make it infinitesimal at a point.
:U1/analysis/oefseq.en
exo=epsilon&qnum=3&qcmlevel=3
20
1
Sequences
epsilon.
:U1/analysis/oefseq.en
exo=comp&exo=2lim&qnum=3&qcmlevel=3
20
1
Sequences
limit and comparison.
:U1/analysis/oefseq.en
exo=cvdiff&exo=cvratio&qnum=4&qcmlevel=3
20
1
Sequences
convergence and terms.
:U1/analysis/grconv.en
level=1&repeat=3
10
0.8
Graphic convergence I
determine the limit of a recursive sequence according to the graph of the function.
:U1/analysis/grconv.en
level=3&repeat=3
10
1.3
Graphic convergence II
determine the limit of a recursive sequence according to the graph of the function.
:U1/analysis/grconv.en
level=4&repeat=3
10
1.6
Graphic convergence III
determine the limit of a recursive sequence according to the graph of the function.
:U1/analysis/dialderiv.en
qnum=3&qcmlevel=3
10
1.2
Derivative dialog
ask questions to get information in order to compute derivatives.
:U1/analysis/minmax.en
ask_type=-30price
10
0.6
Min-Max
maximal profit.
:U1/analysis/minmax.en
ask_type=-20axecut
10
0.6
Min-Max
line and coordinate axes.
:U1/analysis/minmax.en
ask_type=-10pt2cv
10
0.6
Min-Max
minimal distance between a point and a curve.
:U1/analysis/minmax.en
ask_type=-01integral
20
0.8
Min-Max
minimum/maximum of an integral.
:U1/analysis/tafcalc.en
level=2
20
1
Mean Value Theorem
a computing exercise on Mean Value Theorem.
