AP Calculus THANKSGIVING BREAK Take-Home Quiz

This assignment is worth a quiz grade and is due Monday, December 1st at the start of class. Failure to turn it in will result in a zero. Be resourceful you may use

your notes and book. All work must be shown to receive credit.

Throwback to Limits: Evaluate the following limits.

1. lim!→!!!

!!!!!!

2. lim!→!!!!!!!

3. lim!→!! 𝑥 − 2; Why do we not consider evaluating lim!→!! 𝑥 − 2

4. lim!→!!!!!!""!!!

5. lim!→! 5+!!+ !"

!!

6. lim!→!!"#!!!

Continuity: Determine whether the following functions are continuous at a. Use the continuity checklist to justify your answer.

7. 𝑓 𝑥 = 𝑥 − 2;𝑎 = 1

Derivatives: Find f’(x), f”(x), and f(3)(x) for the function.

8. 𝑓 𝑥 = !!!!!!!!!!

Find the derivatives of the following functions.

9. 𝑓 𝑥 = 15𝑒!!

10. ℎ 𝑥 = (!!!)(!!!!!)(!!!!)

11. 𝑦 = !!!! !"#$!"#$!!

12.  𝑦 = tan 𝑒!

13. 𝑦 = 𝜃! sec 5𝜃

14. 𝑦 = 1+ 𝑐𝑜𝑡!𝑥

15. 𝑓 𝑥 = ln 𝑠𝑒𝑐!𝑥𝑡𝑎𝑛!𝑥

16. 𝑓 𝑥 = csc!!(2𝑢 + 1)

Use implicit differentiation to find !"!".

17. 6𝑥! + 7𝑦! = 13𝑥𝑦

18. Find the slope of the curve at the given point. 𝑦! + 3𝑥 = 2; −1, 5 Related Rates:

19. A circle has an initial radius of 50ft when the radius begins decreasing at a rate of 2ft/min. What is the rate of change of the area at the instant the radius is 10ft?

Application of the derivative: Find the critical points of f on the given interval. Then determine the absolute extreme values of f on the given interval. 20. 𝑓 𝑥 = 𝑐𝑜𝑠!𝑥 on [0,𝜋]