The function

The principal part, for , of is

What is the infinite order of the sequence for with respect to the reference ?

Answer:

Note: the entered answer must be an integer; enter 10000 for , enter -10000 for , enter 999 for 'does not exist'.

What is the result of the limit ?

Answer:

Note: the entered answer must be an integer; enter 10000 for , enter -10000 for , enter 999 for 'does not exist'.

The Taylor expansion, of order 2 and with center , of the function is

Let be a function of class , infinitesimal for and with an inflection point with horizontal tangent at . Suppose that not all derivatives of vanish at . Then it is NOT necessarily true that

Let and let be its inverse function. Then equals

Given the function , which of the following statements is true?

Let be a differentiable function such that , , and let . What is the value of ?

Answer:

Note: the entered answer must be an integer; enter 10000 for , enter -10000 for , enter 999 for 'does not exist'.

Let be of class , and let . The condition , for the existence of an inflection point with horizontal tangent, is