Calculus I (AB): Mid-year Derivative Review

Evaluate each of the following derivatives:
Difficulty Rating: 

(a)    Don't forget to take the derivative of the exponent and that (with exponential functions) the original function also appears in the derivative. (b)    When taking the derivative of a logarithm with a base other than e, you need to divide by the ln of the base in the denominator of the derivative. (c)    Don't forget to apply the chain rule and multiply by the derivative of cot x. (d)    This one has a lot of steps with the chain rule. You have to multiply by the derivative of arcsin and the derivative of what's inside it.

---

Calculus II (BC): Convergent S eries

Determine which of the following series converge and (if possible) give the sum:
Difficulty Rating: 

---

Solution: (a)    Apply the Ratio Test. Since the limit is less than 1, the series converges. There is no easy way to find the sum of this series.

(b)    Begin by factoring out the 2/3. This makes it much more obvious that the series is geometric, with a ratio of 1/3.