Infinitely differentiable functions are also called as smooth functions in mathematics. Any analytic function of a real argument is smooth, but the converse is not true. An analytic function is a function given by a convergent power series. A function is analytic only if its Taylor series about x0 converges to the function for every x0 in its domain. Such as all polynomials, exponential function, trigonometric functions, logarithm, and the power functions.

The most difficult question for me on midterm is the fourth question. Although there is a hint, I did not get it. Because f”(t), f'(t) and f(t) made the question looks complicated, I was thinking to use FTC all the time but did not open my mind through the hint.

Study Tips:

1. Mark problems you feel uncomfortable when doing weekly webworks. Redo those questions before midterm.
2. Memorize definitions of theorems and redo classic examples from workshops or recitations.