The Classe Prépa Math for Grandes Écoles is uniquely French pedagogy – very rigorous based on solid abstract theories.
In this lecture the young French professor demonstrates how to teach students the rigorous Math à la Française:
THEOREM 1 :
Note: The ‘x’ in f (x) is hence f is ‘fixed’ by a value
In the above mistake:
is not fixed, but depends on ‘n’. It is wrong to apply Theorem 1.
Note: q is a fixed value.
Reason: is not fixed value but depends on variable ‘n’. It is wrong to apply Theorem 2.
3rd Mistake: Binomial
Expanding the binomial,
Note: valid if k is fixed value.
Reason: k in the is not fixed, it varies from k = 0 to n
Note: p is fixed value.
Reason: n is variable to infinity.
Is below correct ?
[Hint] n is variable, is fixed value.
Final Solution: Exponential
THEOREM 6: From equivalence () to find Limit (), and vice-versa
Converse is true only if
Therefore (from Theorem 6):
Since exponential function is continuous at 1 (why must state the condition of Continuity? )
hence, from [*], we have: