Post on 12-Mar-2021
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!β!!!
!!!!!!
2. lim!β!!!!!!!
3. lim!β!! π₯ β 2; Why do we not consider evaluating lim!β!! π₯ β 2
4. lim!β!!!!!!""!!!
5. lim!β! 5+!!+ !"
!!
6. lim!β!!"#!!!
Continuity: Determine whether the following functions are continuous at a. Use the continuity checklist to justify your answer.
7. π π₯ = π₯ β 2;π = 1
Derivatives: Find fβ(x), fβ(x), and f(3)(x) for the function.
8. π π₯ = !!!!!!!!!!
Find the derivatives of the following functions.
9. π π₯ = 15π!!
10. β π₯ = (!!!)(!!!!!)(!!!!)
11. π¦ = !!!! !"#$!"#$!!
12. π¦ = tan π!
13. π¦ = π! sec 5π
14. π¦ = 1+ πππ‘!π₯
15. π π₯ = ln π ππ!π₯π‘ππ!π₯
16. π π₯ = csc!!(2π’ + 1)
Use implicit differentiation to find !"!".
17. 6π₯! + 7π¦! = 13π₯π¦
18. Find the slope of the curve at the given point. π¦! + 3π₯ = 2; β1, 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. π π₯ = πππ !π₯ on [0,π]