Which among the following statements is the strongest that is true?

A If a function is defined for all x and has a Maclaurin series, then this Maclaurin series converges for all x.

B If a function is defined for all x and has a Maclaurin series, then this Maclaurin series is equal to the function for all x.

C If a function is defined for all x and has a Maclaurin series, then this Maclaurin series is equal to the function for infinitely many values of 

D If a function is defined for all x and has a Maclaurin series, then this Maclaurin series is equal to the function at .

Let’s say  are the first 4 terms of the Maclaurin series of some function . What is ?

Let’s say  is the Maclaurin series of . What is ?

You really should know the Maclaurin series for ,  and  by heart. Let’s see whether you do. Let’s say  is the Maclaurin series of . What is ?

Theorem [Taylor’s formula] Let  be a function that is  times differentiable in an interval containing  and . Then  for some number  between  and . 

Let be any square matrix. It turns out that the determinant of is equal to . Here , the trace of ,  is the sum of the entries of on the main diagonal. 

 What letter is missing here?

What are the constants in the first four terms of the Maclaurin series of ? Input in the form .

What is