Chapter 3 – Part 1: THE DERIVATIVE
Unit 2 Packet
[pic]
[pic]
Calculus Homework NAME _________________________________
Derivatives and Limit Review
1. [pic]
2. If [pic], which of the following are true statements?
I. [pic] is continuous at x = 0.
II. [pic] is differentiable at x = 0.
III. [pic]
3. Let b > 0 be a fixed constant. Then [pic]
*JUST TELL WHAT #3 means, YOU WILL NOT BE ABLE TO “DO” IT*
4. Let [pic]be defined as follows, where [pic]:
[pic]
Which of the following are true about f?
[pic][pic]
[pic]I. [pic]exists.
[pic]II. [pic]exists.
[pic]III. [pic]is continuous at [pic].
A) I only B) II only C) I and II only D) All three are true E) None are true
5. [pic]
A) 0 B) [pic] C) [pic] D) [pic] E) [pic]
6. [pic]
A) 0 B)[pic] C) [pic] D) [pic] E) Does not exist
7. [pic]
A) 1 B) 6 C) 0 D) –1 E) Does not exist
8. Let [pic] Find a value of a so that h is continuous at [pic].
A) [pic] B) [pic] C) [pic] D) [pic]
E) It is not possible to find a value of a so that [pic]is continuous at [pic]
9. If [pic] is continuous at [pic], then [pic]
A) 3 B) –3 C) 0 D) 6 E) –6
10. [pic]
A) 0 B) 1 C) –1 D) [pic] E) [pic]
11. The graph of which function has [pic] as an asymptote?
A) [pic] B) [pic] C) [pic] D) [pic] E) [pic]
12. [pic]
13. The [pic]at x = 3 is:
A) 0 B) 1 C) 3 D) –1 E) nonexistent
14. If y = 7 is a horizontal asymptote of a rational function, f, then which of the following must be true?
[pic]
15. [pic]is:
[pic]
Position, Velocity, and Acceleration
1. A balloonist drops a sandbag from a balloon 160 feet above the ground. After t seconds, the sandbag is 160-16t2 feet above the ground.
a) Find the velocity of the sandbag at t=1.
b) With what velocity does the sandbag hit the ground?
2. A projectile is fired directly upward from the ground with an initial velocity of 112ft/sec. Its distance above the ground after t seconds is 112t-16t2 feet.
a) Find the velocity of the projectile at t = 2, t=3, and t=4.
b) When does the projectile hit the ground?
c) Find the velocity at the instant it hits the ground.
3. A projectile is shot upward from the surface of the earth with and initial velocity of 384 ft/sec. If s(t)= 384t-16t2, what it its velocity after 5 seconds? After 10 seconds?
4. A pebble is dropped from a height of 600 feet. If s(t)=600-16t2, find the pebble’s velocity when it hits the ground.
5. A ball is thrown straight down from the top of a 220 foot building with an initial velocity of –22 ft/sec. If s(t)=220-22t-16t2,
a) What is the velocity after 3 seconds?
b) What is its velocity after falling 108 feet?
6. A ball is dropped from a height of 100 feet and s(t) = 100-16t2 ft/sec. One second later another ball is dropped from a height of 75 feet and s(t)=75-16t2 ft/sec. Which one hits the ground first?
7. An object is dropped from a balloon which is stationary at 1600 ft. Express its height above the ground as a function of t. (Hint: Look at the pattern of the equations in 1-6). How long does it take the object to reach the ground?
8. A ball is thrown vertically upward from the ground with an initial velocity of 60 ft/sec. How high will the ball go?
9. A ball is thrown upward with an initial velocity of 64ft/sec from a height of 80 ft.
a) Find the position function for this motion.
b) When will the ball hit the ground?
................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.
Related searches
- chapter 1 the nature of science
- chapter 1 the first americans
- the outsiders chapter 3 pdf
- the outsiders chapter 3 questions
- the outsiders chapter 3 summary
- 1 john chapter 3 summary
- chapter 3 1 what is ecology
- 1 john chapter 3 explained
- the outsiders chapter 3 quiz
- chapter 1 the sociological perspective
- chapter 1 the woodworking industry
- chapter 3 the outsiders pdf