Retard

This is a short list of the common mistakes I saw when correcting your exercises. So: read it and be careful!!! • When you multiply a number by a negative number, you usually forgot the parenthesis. They ARE important. You can NOT forget them. Example: you write: (e−x ) = e−x · −x That’s WRONG!!!! It should be: (e−x ) = e−x · (−x) You might think: come on, is that important? And I say: YES! IT IS!!! Because if you write it in your way (3 + 2x) · −x you usually do then 3 + 2x − x = 3 + x instead of doing the correct way: (3 + 2x) · (−x) = −3x − 6x2 • You usually say: if x is such that f (x) = 0, then x is an inflection point. WRONG!!! To be an inflection point (if f is 2 times differentiable) f (x) must change the sign! This means that if x is an inflection point, then f (x) = 0, but NOT the opposite. An example: f (x) = x4 It is clear that x = 0 is a minimum (because f (x) is always strictly bigger than 0 if x = 0, and f (0) = 0). If 0 is a minimum, it can NOT be an inflection point. But however f (0) = 0. So, we found one point such that the second derivative is 0 but it is not an inflection point. • f (x) · g(x)dx = f (x)dx · g(x)dx. I have seen in the last test that A LOT of people did things like: xex dx = or x dx = ex xdx ex dx xdx · ex dx

That’s ABSOLUTELY (and sadly) WRONG!!!!!!!!!!!!! If you want to integrate these functions, you have to find alternative (more difficult) ways to do it. Yes, I agree that it would be nicer and easier to do it in this way. . . , but I’m sorry: you CAN NOT do it. • If A and B are matrices, you usually do: A · B = B · A. FALSE!!!!!!! In general, we have that A · B = B · A 1

• You also do many times: if we want to find the matrix X in the equation AX = B, we simply divide by A and. . . X= B . A

Thats a BIG BIG BIG mistake!!! You have to pre-multiply by A−1 at both sides of the equation: A−1 AX = A−1 B to get In X = A−1 B (where In is the identity matrix) and whence X = A−1 B.

1 If we write A , we do NOT know if it is...