Patterning the World: Connecting Mathematics and Science – Spring 2014
The web-site for an interdisciplinary program that integrates introductory math and physics by finding, generating, and quantifying patterns
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Reading Responses and Reflection 3 – Due 6pm Sun. Apr. 20
The reading assignment this week is precalculus Ch 3.4, 3.5 with background reading in Ch 1.1, 1.2, and 1.6. Physics reading is Ch 3.1, 3.2, and 3.4. Remember to fill in all entries below - what you don't know after reading the texts is just as important to us as what you do.
Lastname, Firstname
*
Precalculus Reading
1. Give a short phrase in english that expresses the behavior of the function f indicated by the notation (as x → ∞, f(x) → 3),
2. What is the reciprocal of the expression x
^{2}
+ 3 ? As needed, use ^ to express a power and sqrt() to represent a square root (e.g., sqrt(2) is the square root of 2). Be sure to parenthesize your expression properly.
3. What is the inverse of the function f(x) = x
^{2}
+ 3? In your answer use g as the name of the inverse function (rather than f
^{-1}
). As needed, use ^ to express a power and sqrt() to represent a square root. Be sure to parenthesize your expression properly.
4. What is the domain of the inverse function of f(x) = x
^{2}
+ 3? Use an english phrase to express your answer.
Physics Reading
1. Fig. 3.38 (p.103) represents some of the most important concepts in this section. Study this figure closely.
1. a) What does this figure represent about the motion in the x-direction (horizontally)? Discuss specifically the x-components of velocity and acceleration (e.g. positive/negative/zero, increasing/decreasing).
1. b) What does this figure represent about the motion in the y-direction (vertically)? Discuss specifically the y-components of velocity and acceleration (e.g. positive/negative/zero, increasing/decreasing).
1. c) How does this figure represent the independence of perpendicular motions?
2. Eqs. (3.33), (3.34), and (3.35) describe the horizontal motion of an object in free-fall.
2. a) Briefly describe the meanings of each symbol in these equations. Also note any questions you have.
3. Eqs. (3.36), (3.38), (3.39), and (3.40) describe the vertical motion of an object in free-fall.
3. a) Briefly describe the meanings of each symbol in these equations. Also note any questions you have.
4. Consider the situation depicted in Fig. 3.6 (p. 87), which shows two balls that start moving at the same time. The ball on the left is dropped from rest. The ball on the right is launched with initial horizontal velocity. Assume both balls start from the same distance above the ground, and that air resistance is negligible.
4. a) Which ball hits the ground first?
Left
Right
Same time
Not enough information
Don't know how to tell
Reflections
What would you like us to spend class time on from the precalculus readings?
What would you like us to spend class time on from the physics readings?
What material from the past week (or before) are you still having difficulty with? (Please do let us know, but also try to take advantage of all your resources: QuaSR, study groups, appointments with faculty, on-line tutorials & videos, etc.)
Prompt 1: Describe an instance or instances where you improved your ability to attend to precision. (#5) Provide specific details or examples from your work in the program.
Prompt 2: Describe an instance or instances where you improved your ability to obtain, evaluate, and communicate information. (#9)