***Exercise 1 : When taking the limit of the form f(x)^g(x) you cannot take the limit of the exponent first, i.e. people saying g(x)->0 so lim f(x)^g(x) = lim f(x)^0 = lim 1 = 1 or the other way around lim f(x)^g(x) = lim 0^(g(x)) = lim 0 = 0 which in particular makes limits of the form 0^0 give us 0=1.


L'Hôpital rule is on an indeterminate QUOTIENT of an indeterminate form, it does not apply to products 0xinfinity, one has to transform the product into a quotient (example here lim(x->0) sin(x)ln(x) is not lim(x->0)cos(x)/x), it does not apply when the quotient is not indeterminate as well.


***Exercise 2 : I had some confusing justifications as to why the first function has no absolute maximum/minimum, the fact that it is a continuous function on a non bounded interval alone is not enough, we need the assumption that it is a polynomial, or just simply compute the limits.


Always check the singular points and the bounds of the domains when they exist, 0 and +-2 were forgotten a lot in the second function.


***Exercise 3 : For the inflection points, they are zeroes of the second derivative, but they don't have to zeroes of the first one, the square roots of 3 were often forgotten.

The oblique asymptote was omitted a few times as well but I think you went over this point in class.