AP Calculus January 8, 2009
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The document discusses properties of integrals and the Fundamental Theorem of Calculus. The Fundamental Theorem of Calculus states that integrating the derivative of a function over an interval gives the total change in the function over that same interval. It also provides examples of using integrals to find the total change in position of objects moving along a line given their rate of change functions.
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Practice Problems
Skills Practice
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x f (x)
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1 43
4 19
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3. Give the equation of the linear function that generates the following table of values. Write
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t C(t)
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15 -900
20 -725
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form.
Introductory Algebra Lesson 11 – Linear Functions, Part 2
5. Give the equation of the linear function shown below. Write your answer in slope-intercept
form.
6. Give the equation of the linear function shown below. Write your answer in slope-intercept
form.
7. Give the equation of the linear function shown below. Write your answer in slope-intercept
form.
Introductory Algebra Lesson 11 – Linear Functions, Part 2
8. Give the equation of the linear function shown below. Write your answer in slope-intercept
form.
9. Give the equation of the linear function shown below. Write your answer in slope-intercept
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10. Give the equation of the linear function shown below. Write your answer in slope-intercept
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14. Give the equation of the y-axis. _______________
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16. Give the equation of the line passing through the point (6, 0) that is parallel to y = x
2
3
9 .
17. Give the equation of the line passing through the point (10, 3) that is perpendicular to
1
5
2
xy .
18. Give the equation of the line passing through the point (-12, -1) that is perpendicular to
xy 43 .
Introductory Algebra Lesson 11 – Linear Functions, Part 2
19. Draw an accurate graph of the linear equation 2x + 3y = 6.
Slope-Intercept Form:
Slope: ___________
Vertical Intercept: ____________
Horizontal Intercept: ____________
Two additional points on the line:
____________ _____________
20. Draw an accurate graph of the function 155 yx
Slope-In.
Design of recumbent elliptical trainer
1) A 4-bar linkage mechanism is used to design a recumbent elliptical trainer to rehabilitate people with lower extremity mobility restrictions. The linkage converts rotational motion to an elliptical trajectory.
2) The 4-bar linkage mechanism has one degree of freedom according to Grubler's equation. An elliptical trajectory is achieved by connecting the legs to the point that traces an ellipse during the linkage's back-and-forth motion.
3) Velocity and acceleration are derived using velocity and acceleration diagrams from the 4-bar linkage mechanism. The slider's velocity is calculated as 1.6756 m/s and acceleration is -3.5975 m/s2 using D'Alembert's principle
Week 10 part2 pe 6282
The document discusses transfer functions and Laplace transforms. It explains that transfer functions provide a simple way to relate the input and output of a system by describing the relationship as a ratio of outputs to inputs in the Laplace domain. Common examples of transfer functions for different system elements are provided, such as gears, amplifiers, and DC motors. It also discusses how to calculate overall transfer functions for systems consisting of multiple elements in series and systems with feedback loops.
Finite element analysis sdfa ggq rsd vqer fas dd sg fa sd qadas casdasc asdac...
Finite element analysis sdfa ggq rsd vqer fas dd sg fa sd qadas casdasc asdac...MrGChandrasekarmecha
sdfa ggq rsd vqer fas dd sg fa sd qadas casdasc asdac asascasasGenerics With Swift
The document discusses generics in Swift. It provides examples of using generics to write functions that can swap or operate on values of any type rather than being limited to a specific type. The document compares generics to using protocols, noting some key differences in how the return value is handled. It also discusses challenges with using generics with some frameworks like TableViews due to bugs, as well as examples of using generics for things like API requests, object mapping, and completion handlers. Overall it advocates that generics are fast, useful, flexible and practical despite some limitations.
Three Solutions of the LLP Limiting Case of the Problem of Apollonius via Geo...
This document adds to the collection of solved problems presented in http://www.slideshare.net/JamesSmith245/rotations-of-vectors-via-geometric-algebra-explanation-and-usage-in-solving-classic-geometric-construction-problems-version-of-11-february-2016,http://www.slideshare.net/JamesSmith245/solution-of-the-ccp-case-of-the-problem-of-apollonius-via-geometric-clifford-algebra, http://www.slideshare.net/JamesSmith245/solution-of-the-special-case-clp-of-the-problem-of-apollonius-via-vector-rotations-using-geometric-algebra, and http://www.slideshare.net/JamesSmith245/a-very-brief-introduction-to-reflections-in-2d-geometric-algebra-and-their-use-in-solving-construction-problems. After reviewing, briefly, how reflections and rotations can be expressed and manipulated via GA, it solves the LLP limiting case of the Problem of Apollonius in two ways.
Robotics lec 6
This document discusses different approaches for generating smooth motion trajectories for robot arms between an initial and final pose. It covers:
1) Joint interpolation, which interpolates between initial and final joint angle values to move each joint along a smooth path.
2) Cartesian interpolation, which interpolates directly between initial and final end-effector poses in Cartesian space, computing inverse kinematics at each step.
3) Examples of applying these approaches in both 2D and 3D, including generating sample trajectories for a PUMA robot arm.
v1chap1.pdf
1) The document discusses units and vectors, which are fundamental tools in physics. It introduces the International System of Units (SI units) including common units like meters, seconds, kilograms.
2) Vectors are quantities that have both magnitude and direction, and can be represented graphically or through components. The document covers how to add and multiply vectors through their components and graphically.
3) It also discusses scalar and vector products of vectors, as well as changing units and dimensional analysis, which are important concepts for solving physics problems.
Single Pendulum Gantry (SPG) 2013.4.17
This document describes an experiment involving controlling a single pendulum rod suspended in front of a linear cart using state feedback control. The group derived the nonlinear and linearized equations of motion for the system. They represented the system in state space form and used pole placement design to place the closed-loop poles in order to meet design specifications of less than 5% overshoot and a settling time of less than 2.2 seconds. The group determined the state space matrices A, B, C, and D and used Matlab to simulate the pole-placement based controller.
Lar calc10 ch02_sec2
This document discusses basic differentiation rules and rates of change. It introduces the constant rule, power rule, constant multiple rule, sum and difference rules, derivatives of sine and cosine functions, and using derivatives to find rates of change such as velocity and acceleration. Examples are provided to demonstrate finding derivatives of various functions and using derivatives to calculate average velocity and velocity from a position function.
Lar calc10 ch04_sec4
This document discusses the Fundamental Theorem of Calculus, which connects differentiation and integration. It states that differentiation and integration are inverse operations, analogous to how multiplication and division are inverse. The document provides examples of using the Fundamental Theorem to evaluate definite integrals and find average values. It also introduces the Second Fundamental Theorem of Calculus and the Net Change Theorem, which relate integrals and antiderivatives.
DSP System Assignment Help
I am Martin J. I am a DSP System Assignment Expert at matlabassignmentexperts.com. I hold a Master's in Matlab, University of Maryland. I have been helping students with their assignments for the past 10 years. I solve assignments related to the DSP System.
Visit matlabassignmentexperts.com or email info@matlabassignmentexperts.com.
You can also call on +1 678 648 4277 for any assistance with DSP System Assignment.
Tarea1
This document contains several multi-part calculus problems involving estimating areas under curves using Riemann sums with rectangles. The problems ask the student to:
- Estimate areas under graphs using left, right, and midpoint Riemann sums with varying numbers of rectangles
- Interpret Riemann sums as approximations of definite integrals involving the area under a curve
- Evaluate definite integrals using properties such as interpreting them in terms of areas under curves
Curve modeling bezier curves
This document discusses Bézier curves and their properties. It begins by stating that traditional parametric curves are not very geometric and do not provide intuitive shape control. It then outlines desirable properties for curve design systems, including being intuitive, flexible, easy to use, providing a unified approach for different curve types, and producing invariant curves under transformations. The document proceeds to discuss Bézier, B-spline and NURBS curves which address these properties by allowing users to manipulate control points to modify curve shapes. Key properties of Bézier curves are described, including their basis functions and the fact that moving control points modifies the curve smoothly. Cubic Bézier curves are discussed in detail as a common parametric curve type, and
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Week 10 part 3 pe 6282 mecchanical liquid and electrical
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Reduction of multiple subsystem [compatibility mode]
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Finite element analysis sdfa ggq rsd vqer fas dd sg fa sd qadas casdasc asdac...
Finite element analysis sdfa ggq rsd vqer fas dd sg fa sd qadas casdasc asdac...
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Behind Their Eyes v1
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Walk into any classroom and watch the breakneck pace at which teachers are working hard to help students learn. Mind you, if we don’t uncover what students are thinking while learning, they may be running down the wrong path. OK, so we need ways to make student thinking visible. Seeing their thinking is important, but we also need to create the time and space for teachers to absorb, reflect, and act on what their students thinking reveals. This workshop shares strategies both for making student thinking visible and for creating time and space for teachers to meaningfully act on what they learn about what’s going on behind their eyes.
Leading Change v1
“If you really want to understand something, try changing it.” - Kurt Lewin
As the Director of Learning for a school division made up of 18 schools, my job is to help lead the largest change initiative ever undertaken in our school community. One of the most important, difficult, messy things any school leader does is lead change. While we can learn from the change leadership of others, copying their work most often leads to failure. Success is more likely to come from adapting others work to our own context. In this workshop I share the journey we’ve undertaken collectively in our schools; how we developed a shared vision, cultivated collaborative cultures, maintained a focus on deep learning, and wrestle with the nuances of accountability. Informed by the latest research on change management in education, we also model strategies for fostering deep learning conversations in your schools. We’ll engage in some deeper learning conversations together and take back a wealth of ideas you can adapt to your own context. Developing collaborative cultures is careful and precise work that has profound impact when carried out well. So how do you do that? Come, let’s learn together. Good people are important, but good cultures are moreso.
Providing Permission To Wonder v2.1
In a world where knowledge is more a verb than a noun how do we foster deep learning in our students? Good questions cause thinking. Unfortunately, many of the questions regularly asked in classrooms focus on knowledge as a noun. This presentation will explore inquiry as a pedagogical stance and the effective use of thinking and learning tools in the classroom. We will work together to model teaching practices that lead to students co-constructing a networked (real world) rather than hierarchical (artificial) understanding of their world regardless of grade level or discipline.
Participants will leave this workshop with a toolkit of research based questioning and thinking strategies they can begin using with their students tomorrow.
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The document is a presentation about digital citizenship given by Darren Kuropatwa at the Building Learning Communities Conference in Boston, MA in July 2017. It discusses the importance of digital citizenship and responding to adversity with persistent kindness. It provides examples of digital citizenship issues and scenarios for discussion. It encourages participants to think about their own digital footprint and how to be good digital citizens.
Digital Storytelling for Deeper Learning v1
Presented at the Riding the Wave Conference in Gimli, Manitoba. May 2017.
In two words, you remember the whole story: glass slipper, sour grapes, cold porridge. You remember more than facts, you recall relationships & deeper connections between characters. Some of the powerful ways we leverage digital for deeper learning includes challenging sources of information (fake news), exploring bias (developing empathy through multiple perspectives), and creating powerful feedback loops that foster deeper learning.
Powerful narratives, in a word or two, bring to mind a wealth of ideas & relationships; more than just facts. How can we find stories that make our teaching sticky and help kids find, and more importantly tell, stories that make learning stick? This workshop will equip teachers with the skills & knowledge to foster deeper learning across the curriculum by intentionally leveraging digital tools to foster deeper learning.
Tales of Learning and the Gifts of Footprints v4.2
This document appears to be a presentation about digital learning and storytelling. It discusses shifting from compliance to care, private to public learning, and consumer to participatory models. It addresses what digital storytellers look like and principles of learning including starting where students are, learning being done by and for students, students talking about learning, having learning targets, and feedback. It encourages generosity, sharing tales of learning, and giving the gifts of footprints.
The Fourth Screen v4.2
Presented at the Richmond District Conference, Feb 2017.
A series of stories woven together to start a conversation with middle and high school students, teachers, and parents about living our lives on and offline (on The Fourth Screen) more thoughtfully.
This talk focuses primarily on the ideas of Empathy, Empowerment & Persistent Kindness and shares resources teachers can use to lead these sorts of conversations with their own students.
Making Student Thinking Visible v4
Slides to support a master class on making student thinking visible through practical hands-on activities and structured around Dylan Wiliam's work on formative assessment and active learning. Held at the BYTE Conference 2017 in Portage la Prairie, Manitoba.
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A group of educators from the BYTE Conference 2017 (Build Your Teaching Experience) share their ideas about learning as a series of visual metaphors they found on their phones.
Leveraging Digital for Deeper Learning
Slides to support a Keynote presentation to Early Years and Middle Years teachers in Hanover School Division on 3 February 2017.
We Learn Through Stories at PRIZMAH17
The document discusses storytelling and how it can be used as a tool for learning. It suggests that storytelling allows students to think in metaphors and learn through stories. It provides examples of how digital tools like QR codes and apps can be used to incorporate storytelling into the classroom. It also outlines some rules of thumb for using storytelling, such as personalizing tasks to students' experiences, collaborating on group projects, and getting feedback from both inside and outside the classroom.
Providing Permission to Wonder v3
In a world where knowledge is more a verb than a noun how do we foster deep learning in our students? Good questions cause thinking. Unfortunately, many of the questions regularly asked in classrooms focus on knowledge as a noun. This presentation will explore the effective use of thinking and learning tools in the classroom. We will work together to model teaching practices that lead to students co-constructing a networked (real world) rather than hierarchical (artificial) understanding of their world regardless of grade level or discipline.
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The Fourth Screen v4.1
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Slides to support a master class on making student thinking visible through practical hands-on activities and structured around Dylan Wiliam's work on formative assessment and active learning.
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A group of educators from the Anderson Union High School & Redding School Districts and share their ideas about learning as a series of visual metaphors.
Providing Permission to Wonder v2
In a world where knowledge is more a verb than a noun how do we foster deep learning in our students? Good questions cause thinking. Unfortunately, many of the questions regularly asked in classrooms focus on knowledge as a noun. This presentation will explore the effective use of thinking and learning tools in the classroom. We will work together to model teaching practices that lead to students co-constructing a networked (real world) rather than hierarchical (artificial) understanding of their world regardless of grade level or discipline.
Participants leave this workshop with a toolkit of research based questioning and thinking strategies they can begin using with their students tomorrow.
The Fourth Screen v4
This document contains a collection of images, quotes, and short passages on topics related to online communities, sharing, and empowerment through technology. The snippets discuss how the internet allows information to be easily shared, encourages learning, and can help empower victims of bullying. The overarching theme is about the positive impact community and connection through online platforms can provide.
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A group of educators at the Building Learning Communities Conference share their ideas about learning as a series of visual metaphors.
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Slides to support a master class at the Building Learning Communities Conference in Boston, MA. 18 July 2016.
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The recent surge in pro-Palestine student activism has prompted significant responses from universities, ranging from negotiations and divestment commitments to increased transparency about investments in companies supporting the war on Gaza. This activism has led to the cessation of student encampments but also highlighted the substantial sacrifices made by students, including academic disruptions and personal risks. The primary drivers of these protests are poor university administration, lack of transparency, and inadequate communication between officials and students. This study examines the profound emotional, psychological, and professional impacts on students engaged in pro-Palestine protests, focusing on Generation Z's (Gen-Z) activism dynamics. This paper explores the significant sacrifices made by these students and even the professors supporting the pro-Palestine movement, with a focus on recent global movements. Through an in-depth analysis of printed and electronic media, the study examines the impacts of these sacrifices on the academic and personal lives of those involved. The paper highlights examples from various universities, demonstrating student activism's long-term and short-term effects, including disciplinary actions, social backlash, and career implications. The researchers also explore the broader implications of student sacrifices. The findings reveal that these sacrifices are driven by a profound commitment to justice and human rights, and are influenced by the increasing availability of information, peer interactions, and personal convictions. The study also discusses the broader implications of this activism, comparing it to historical precedents and assessing its potential to influence policy and public opinion. The emotional and psychological toll on student activists is significant, but their sense of purpose and community support mitigates some of these challenges. However, the researchers call for acknowledging the broader Impact of these sacrifices on the future global movement of FreePalestine.
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AP Calculus January 8, 2009
- 1. Properties of Integrals Acme adding machine
- 3. What does The Fundamental Theorem of Calculus say? Let the function ƒ be continuous on [a, b] with derivative ƒ'. Then ... Total change in ƒ In words: Integrating a rate of change function ƒ' over an interval [a, b] gives the total change in ƒ, ƒ(b) - ƒ(a), over the same interval. In other words, the integral of a derivative is the same thing as the total change in it's parent function over the same interval. Also recall: and ...
- 4. A particle is traveling along a straight line. Its position is given by Find the change in position from t = 1 to t = 4.
- 5. Suppose a car is moving with non-decreasing speed according to the table below: (a) What is an upper estimate for the distance traveled in the first 2 seconds? (b) Determine upper and lower estimates for the change in position for the first 10 seconds.
- 6. The Fundamental Theorem of Calculus ... part I Let the function ƒ be continuous on [a, b] with derivative ƒ'. Then ... Total change in ƒ In words: Integrating a rate of change function ƒ' over an interval [a, b] gives the total change in ƒ, ƒ(b) - ƒ(a), over the same interval. In other words, the integral of a derivative is the same thing as the total change in it's parent function over the same interval. Also recall: and ...
- 7. Use The Fundamental Theorem of Calculus to evaluate: