Remarks :
Exercise 1 : It was a very confusing question for most students. Some mixed up the notations and didn't differentiate the Taylor polynomial from the one we start with. Some gave a general formula for Taylor series but did not take into account that our function is a polynomial and the derivatives can be computed explicitly.


Exercise 2 : I put a point for the drawing and a point for the rest, and the latter was done correctly nowhere. The only important thing to check is that we can differentiate the function at c and the derivative is 0 at c. Absolutely no one checked that. I gave full point still if everything else was done and clear.

Also some did not bother at least saying that the equality holds for t<c. It is obvious, BUT needs to be mentioned.


Exercise 2.10 18+22 : Generally very good, I took away 1/2 point if no constant was added as it has been the case. I only did it once for the 2 exercises though.

Exercise 2.11 8+15 : Nothing much to say, sometimes the exercise 8 was done a little too briefly, with little to no maths using a formula that outputs the answer directly.

Exercise 3.7 2+13 : Except a few computation mistakes, generally flawless.

Exercise 3.7 16 : I was VERY surprised to see more than half the students failing l'Hôpital rule. We have lim(e->0) (exp((e+1)t)-exp(t))/e, people used l'Hôpital, but differentiate the top half with respect to t and not e so they got a (e+1)exp((e+1)t)-exp(t)) and so a 0 limit. Here we had to differentiate everything with respect to e as it is our parameter going to 0.


Exercise 3.7 18 : A lot of people were unsure on what they had to do. A lot just checked the formula A*exp(r1*t)+B*exp(r2*t), and didn't get that the goal was to prove those formulas.