TeXercises.com

Newton-Verfahren zur Nullstellenbestimmung

About points...

We associate a certain number of points with each exercise.
When you click an exercise into a collection, this number will be taken as points for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit the number of points for the exercise in the collection independently, without any effect on "points by default" as represented by the number here.

That being said... How many "default points" should you associate with an exercise upon creation?
As with difficulty, there is no straight forward and generally accepted way.
But as a guideline, we tend to give as many points by default as there are mathematical steps to do in the exercise.
Again, very vague... But the number should kind of represent the "work" required.

About difficulty...

We associate a certain difficulty with each exercise.
When you click an exercise into a collection, this number will be taken as difficulty for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit its difficulty in the collection independently, without any effect on the "difficulty by default" here.
Why we use chess pieces? Well... we like chess, we like playing around with \(\LaTeX\)-fonts, we wanted symbols that need less space than six stars in a table-column... But in your layouts, you are of course free to indicate the difficulty of the exercise the way you want.

That being said... How "difficult" is an exercise? It depends on many factors, like what was being taught etc.
In physics exercises, we try to follow this pattern:

Level 1 - One formula (one you would find in a reference book) is enough to solve the exercise. Example exercise

Level 2 - Two formulas are needed, it's possible to compute an "in-between" solution, i.e. no algebraic equation needed. Example exercise

Level 3 - "Chain-computations" like on level 2, but 3+ calculations. Still, no equations, i.e. you are not forced to solve it in an algebraic manner. Example exercise

Level 4 - Exercise needs to be solved by algebraic equations, not possible to calculate numerical "in-between" results. Example exercise

Level 5 -
Level 6 -

Exercise

https://texercises.com/exercise/newton-verfahren-zur-nullstellenbestimmung/

Question

Solution

Short

Video

\(\LaTeX\)

No explanation / solution video to this exercise has yet been created.

Visit our YouTube-Channel to see solutions to other exercises.
Don't forget to subscribe to our channel, like the videos and leave comments!

Exercise:
Zur numerischen Bestimmung von Nullstellen der Funktion fx wird ausgeh von einem Startwert x_ iterativ folges Rezept angewet: Zunächst wird die Tangente t_ix an den Graphen von f im Punkt x_i|fx_i betrachtet. S_i+x_i+| ist der Schnittpunkt dieser Tangente mit der x-Achse. abcliste abc Gib die Gleichung der Tangente t_ix an. abc Bestimme den Schnittpunkt x_i+| von t_ix und der x-Achse. abc Gib für folge Funktionen die Iterationsvorschrift an und berechne die ersten Werte der Iteration für den Startwert x_. enumerate item fxx^-x+ item fxx^-x+ item fxx^-x- item fxx^-x^- item fxx^+x^- enumerate abcliste bf Hinweis: Das Newton-Verfahren konvergiert wenn fx in einem Intervall ab das die Nullstelle enthält zweimal stetig differenzierbar mit f'xnot not f''x ist und f streng monoton wachs und f' monoton wachs ist oder f streng monoton fall und f' monoton fall ist.

Solution:
abcliste abc t_ixf'x_ix-x_i+fx_i abc f'x_ix_i+-x_i+fx_iRightarrow x_i+x_i-fracfx_if'x_i abc enumerate item x_i+x_i-fracx_i^-x_i+x_i- x_ x_ x_ x_ x_ item x_i+x_i-fracx^-x+x- x_ x_ x_ x_ x_ item x_i+x_i-fracx_i^-x_i-x_i^- x_ x_ x_ x_ x_ item x_i+x_i-fracx_i^-x_i^-x_i^-x x_ x_ x_ x_ x_ item x_i+x_i-fracx_i^+x_i^-x_i^+x_i x_ x_ x_ x_ x_ enumerate abcliste

Meta Information

\(\LaTeX\)-Code

Contained in these collections:

Attributes & Decorations

Tags	computer, iteration, iterationsvorschrift, konvergenz, mathematik, newton, newton-verfahren, nullstelle, nullstellen, nullstellen-bestimmung, numerik, numerische, pc, rechnergestützte, startwert, tangente, verfahren, wissenschaft
Content image
Difficulty	(3, default)
Points	12 (default)
Language	(Deutsch)
Type	Calculative / Quantity
Creator	uz
Decoration
File
Link