Identità dell'integrazione 7
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.
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 -
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 -
Question
Solution
Short
Video
\(\LaTeX\)
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Don't forget to subscribe to our channel, like the videos and leave comments!
Exercise:
footnotehttps://math.stackexchange.com/questions//functional-inequality-with-egral-functionSia f una funzione continua f:to Dimostra che se fxleq _^xftdt allora fxequiv
Solution:
Per il teorema del valor medio abbiamo che siccome la funzione è continua per ogni x _^xftdtx fcqquad textper qualche cinx Ma dato che la funzione f ha come immagini vale che leq fcleq e quindi fxleq x fcleq x. Da qui facciamo un bootstrap: reinsero questa disequazione in quella di partenza otteniamo fxleq _^xftdtleq _^xtdtx^ e iterando questo procedimento possiamo salire di grado e ottenere fxleq frac^n-n! x^nquad forall noversetntoinftylongrightarrow fxequiv
footnotehttps://math.stackexchange.com/questions//functional-inequality-with-egral-functionSia f una funzione continua f:to Dimostra che se fxleq _^xftdt allora fxequiv
Solution:
Per il teorema del valor medio abbiamo che siccome la funzione è continua per ogni x _^xftdtx fcqquad textper qualche cinx Ma dato che la funzione f ha come immagini vale che leq fcleq e quindi fxleq x fcleq x. Da qui facciamo un bootstrap: reinsero questa disequazione in quella di partenza otteniamo fxleq _^xftdtleq _^xtdtx^ e iterando questo procedimento possiamo salire di grado e ottenere fxleq frac^n-n! x^nquad forall noversetntoinftylongrightarrow fxequiv
Meta Information
Exercise:
footnotehttps://math.stackexchange.com/questions//functional-inequality-with-egral-functionSia f una funzione continua f:to Dimostra che se fxleq _^xftdt allora fxequiv
Solution:
Per il teorema del valor medio abbiamo che siccome la funzione è continua per ogni x _^xftdtx fcqquad textper qualche cinx Ma dato che la funzione f ha come immagini vale che leq fcleq e quindi fxleq x fcleq x. Da qui facciamo un bootstrap: reinsero questa disequazione in quella di partenza otteniamo fxleq _^xftdtleq _^xtdtx^ e iterando questo procedimento possiamo salire di grado e ottenere fxleq frac^n-n! x^nquad forall noversetntoinftylongrightarrow fxequiv
footnotehttps://math.stackexchange.com/questions//functional-inequality-with-egral-functionSia f una funzione continua f:to Dimostra che se fxleq _^xftdt allora fxequiv
Solution:
Per il teorema del valor medio abbiamo che siccome la funzione è continua per ogni x _^xftdtx fcqquad textper qualche cinx Ma dato che la funzione f ha come immagini vale che leq fcleq e quindi fxleq x fcleq x. Da qui facciamo un bootstrap: reinsero questa disequazione in quella di partenza otteniamo fxleq _^xftdtleq _^xtdtx^ e iterando questo procedimento possiamo salire di grado e ottenere fxleq frac^n-n! x^nquad forall noversetntoinftylongrightarrow fxequiv
Contained in these collections
| Title | Creator | Matched on |
|---|---|---|
| Identità dell'integrazione 3 | gl | tagstitle |
| Identità dell'integrazione 4 | gl | tagstitle |
| Identità dell'integrazione 5 | gl | tagstitle |
| Identità dell'integrazione 6 | gl | tagstitle |
| Identità dell'integrazione 8 | gl | tagstitle |
Similar exercises (7)
| Title | Creator | Matched on |
|---|---|---|
| Identità dell'integrazione 3 | gl | tagstitle |
| Identità dell'integrazione 4 | gl | tagstitle |
| Identità dell'integrazione 5 | gl | tagstitle |
| Identità dell'integrazione 6 | gl | tagstitle |
| Identità dell'integrazione 8 | gl | tagstitle |
| Identità dell'integrazione 1 | gl | tagstitle |
| Identità dell'integrazione 2 | gl | tagstitle |

