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Taylor - UNSA MP 2001
power series expansion and Taylor formula.
180 2001
3
U1
analysis, calculus
taylor expansion, order, infinitesimal, convergence, limit, series, polynomial, continuity, derivative


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/taylor.en
types=combin&center=0&order=3
10
0.5
Taylor level 1
linear combination.
:U1/analysis/taylor.en
types=combin&center=1&order=3
10
0.7
Taylor level 2
linear combination again.
:U1/analysis/taylor.en
types=derivsum&types=deriv&types=sumwderiv&center=1&order=3
20
1
Taylor level 3
derivative and linear combination.
:U1/analysis/taylor.en
types=squaresum&types=square&types=derivprod&types=int&types=multderiv&types=mult&types=polynomial&types=sumsquare&center=1&order=3
30
1
Taylor level 4
various formulae.
:U1/analysis/taylor.en
types=compo&types=division&types=reciproc&center=1&order=3
30
1.5
Taylor level 5
inverse function and division.
:U1/analysis/taylor.en
types=compinv1&types=compinv2&types=inv&types=linfrac&center=1&order=3
20
2
Taylor level 6
be careful it's hard!
:U1/analysis/coincdev.en
Degree=2&range=3
20
0.5
Coincidence-Dev level 1
graphically find the Taylor expansion of a function.
:U1/analysis/coincdev.en
Degree=3&range=5
30
1
Coincidence-Dev level 2
graphically find the Taylor expansion of a function.
:U1/analysis/coincdev.en
Degree=4&range=8
20
1.5
Coincidence-Dev level 3
graphically find the Taylor expansion of a function.
:U1/analysis/joint.en
order=2&fundif=3&tolerance=0.001
10
0.7
Joint level 1
parametrize a function to make it differentiable to a required order.
:U1/analysis/joint.en
order=3&fundif=2&tolerance=0.0005
20
1
Joint level 2
parametrize a function to make it differentiable to a required order.
:U1/analysis/joint2.en
order=4&fundif=1&tolerance=0.001
20
1
Joint II
parametrize a function to make it continue or differentiable on 2 points.