AP CAlc take home quiz - Ms. Pytelmspytel.weebly.com/.../3/9/9/3/39938879/take_home_quiz_1.pdfAP...
Transcript of AP CAlc take home quiz - Ms. Pytelmspytel.weebly.com/.../3/9/9/3/39938879/take_home_quiz_1.pdfAP...
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]