This slideshow teaches about combining functions using products and quotients. It provides examples of multiplying two functions together using the formula y=f(x)g(x) and distributing terms. It also discusses how to find restrictions where a factor is equal to zero, and defines domain and range. An example word problem demonstrates how to write a revenue function by multiplying a price function and attendance function.
The closed interval method tells us how to find the extreme values of a continuous function defined on a closed, bounded interval: we check the end points and the critical points.
The closed interval method tells us how to find the extreme values of a continuous function defined on a closed, bounded interval: we check the end points and the critical points.
EVALUATING INTEGRALS.Evaluate the integral shown below. (H.docxgitagrimston
EVALUATING INTEGRALS.
Evaluate the integral shown below. (Hint: Try the substitution u = (7x2 + 3).)
1)
x dx
(7x2 + 3)5
Evaluate the integral shown below. (Hint: Apply a property of logarithms first.)
2)
ln x6
x
dx
1
Use the Fundamental Theorem of Calculus to find the derivative shown below.
3)
d
dx
x5
0
sin t dt
For the function shown below, sketch a graph of the function, and then find the SMALLEST possible value and the
LARGEST possible value for a Riemann sum of the function on the given interval as instructed.
4) f(x) = x2 ; between x = 3 and x = 7 with four rectangles of equal width.
^
CHARACTERISTICS and BEHAVIOR OF FUNCTIONS.
Use l'Hopital's rule to find the limit below.
5) lim
x
5x + 9
6x2 + 3x - 9
^
Use l'Hopital's rule to find the limit below. (Hint: The indeterminate form is f(x)g(x).)
6) lim
x
1 + 2
x3
x
2
Solve the following problem.
7) The 9 ft wall shown here stands 30 feet from the building. Find the length of the shortest straight beam that will
reach to the side of the building from the ground outside the wall.
9' wall
30'
Hint: Let "h" be the height on the building where the ladder touches; let "x" be the distance on the ground
between the wall and the foot of the ladder. Use similar triangles and the Pythagorean Theorem to write the
length of the beam "L" as a function of "x". Also note that a radical function is minimized when it radicand is
minimized.
For the function shown below, identify its local and absolute extreme values (if any), saying where they occur.
8) f(x) = -x3- 9x2 - 24x + 3
3
Find a value for "c" that satisfies the equation f(b) - f(a)
b - a
= f (c) in the conclusion of the Mean Value Theorem for the
function and interval shown below.
9) f(x) = x +
75
x
, on the interval [3, 25]
DERIVATIVES.
Find the equation of the tangent line to the curve whose function is shown below at the given point.
10) x5y5 = 32, tangent at (2, 1)
Use implicit differentiation to find dy/dx.
11) xy + x + y = x2y2
Given y = f(u) and u = g(x), find dy/dx = f (g(x))g (x).
12) y = u(u - 1), u = x2 + x
4
Find y .
13) y = (4x - 5)(4x3 - x2 + 1)
Find the derivative of the function "y" shown below.
14) y =
x2 + 8x + 3
x
Solve the problem below.
15) One airplane is approaching an airport from the north at 163 km/hr. A second airplane approaches from the east
at 261 km/hr. Find the rate at which the distance between the planes changes when the southbound plane is 31
km away from the airport and the westbound plane is 18 km from the airport.
FUNCTIONS, LIMITS and CONTINUITY.
Find the intervals on which the function shown below is continuous.
16) y =
x + 2
x2 - 8x + 7
5
A function f(x), a point c, the limit of f(x) as x approaches c, and a positive number is given. Find a number > 0 such
that for all x, 0 < x - c < f(x) - L < .
17) f(x) = 10x - 1, L = 29, c = 3, and = 0.01
Find all points "x" where the function shown below is discontinuous.
18)
Solve the "composite function ...
* Find zeros of polynomial functions
* Use the Fundamental Theorem of Algebra to find a function that satisfies given conditions
* Find all zeros of a polynomial function
State of ICS and IoT Cyber Threat Landscape Report 2024 previewPrayukth K V
The IoT and OT threat landscape report has been prepared by the Threat Research Team at Sectrio using data from Sectrio, cyber threat intelligence farming facilities spread across over 85 cities around the world. In addition, Sectrio also runs AI-based advanced threat and payload engagement facilities that serve as sinks to attract and engage sophisticated threat actors, and newer malware including new variants and latent threats that are at an earlier stage of development.
The latest edition of the OT/ICS and IoT security Threat Landscape Report 2024 also covers:
State of global ICS asset and network exposure
Sectoral targets and attacks as well as the cost of ransom
Global APT activity, AI usage, actor and tactic profiles, and implications
Rise in volumes of AI-powered cyberattacks
Major cyber events in 2024
Malware and malicious payload trends
Cyberattack types and targets
Vulnerability exploit attempts on CVEs
Attacks on counties – USA
Expansion of bot farms – how, where, and why
In-depth analysis of the cyber threat landscape across North America, South America, Europe, APAC, and the Middle East
Why are attacks on smart factories rising?
Cyber risk predictions
Axis of attacks – Europe
Systemic attacks in the Middle East
Download the full report from here:
https://sectrio.com/resources/ot-threat-landscape-reports/sectrio-releases-ot-ics-and-iot-security-threat-landscape-report-2024/
JMeter webinar - integration with InfluxDB and GrafanaRTTS
Watch this recorded webinar about real-time monitoring of application performance. See how to integrate Apache JMeter, the open-source leader in performance testing, with InfluxDB, the open-source time-series database, and Grafana, the open-source analytics and visualization application.
In this webinar, we will review the benefits of leveraging InfluxDB and Grafana when executing load tests and demonstrate how these tools are used to visualize performance metrics.
Length: 30 minutes
Session Overview
-------------------------------------------
During this webinar, we will cover the following topics while demonstrating the integrations of JMeter, InfluxDB and Grafana:
- What out-of-the-box solutions are available for real-time monitoring JMeter tests?
- What are the benefits of integrating InfluxDB and Grafana into the load testing stack?
- Which features are provided by Grafana?
- Demonstration of InfluxDB and Grafana using a practice web application
To view the webinar recording, go to:
https://www.rttsweb.com/jmeter-integration-webinar
Let's dive deeper into the world of ODC! Ricardo Alves (OutSystems) will join us to tell all about the new Data Fabric. After that, Sezen de Bruijn (OutSystems) will get into the details on how to best design a sturdy architecture within ODC.
Search and Society: Reimagining Information Access for Radical FuturesBhaskar Mitra
The field of Information retrieval (IR) is currently undergoing a transformative shift, at least partly due to the emerging applications of generative AI to information access. In this talk, we will deliberate on the sociotechnical implications of generative AI for information access. We will argue that there is both a critical necessity and an exciting opportunity for the IR community to re-center our research agendas on societal needs while dismantling the artificial separation between the work on fairness, accountability, transparency, and ethics in IR and the rest of IR research. Instead of adopting a reactionary strategy of trying to mitigate potential social harms from emerging technologies, the community should aim to proactively set the research agenda for the kinds of systems we should build inspired by diverse explicitly stated sociotechnical imaginaries. The sociotechnical imaginaries that underpin the design and development of information access technologies needs to be explicitly articulated, and we need to develop theories of change in context of these diverse perspectives. Our guiding future imaginaries must be informed by other academic fields, such as democratic theory and critical theory, and should be co-developed with social science scholars, legal scholars, civil rights and social justice activists, and artists, among others.
Accelerate your Kubernetes clusters with Varnish CachingThijs Feryn
A presentation about the usage and availability of Varnish on Kubernetes. This talk explores the capabilities of Varnish caching and shows how to use the Varnish Helm chart to deploy it to Kubernetes.
This presentation was delivered at K8SUG Singapore. See https://feryn.eu/presentations/accelerate-your-kubernetes-clusters-with-varnish-caching-k8sug-singapore-28-2024 for more details.
DevOps and Testing slides at DASA ConnectKari Kakkonen
My and Rik Marselis slides at 30.5.2024 DASA Connect conference. We discuss about what is testing, then what is agile testing and finally what is Testing in DevOps. Finally we had lovely workshop with the participants trying to find out different ways to think about quality and testing in different parts of the DevOps infinity loop.
GraphRAG is All You need? LLM & Knowledge GraphGuy Korland
Guy Korland, CEO and Co-founder of FalkorDB, will review two articles on the integration of language models with knowledge graphs.
1. Unifying Large Language Models and Knowledge Graphs: A Roadmap.
https://arxiv.org/abs/2306.08302
2. Microsoft Research's GraphRAG paper and a review paper on various uses of knowledge graphs:
https://www.microsoft.com/en-us/research/blog/graphrag-unlocking-llm-discovery-on-narrative-private-data/
Slack (or Teams) Automation for Bonterra Impact Management (fka Social Soluti...Jeffrey Haguewood
Sidekick Solutions uses Bonterra Impact Management (fka Social Solutions Apricot) and automation solutions to integrate data for business workflows.
We believe integration and automation are essential to user experience and the promise of efficient work through technology. Automation is the critical ingredient to realizing that full vision. We develop integration products and services for Bonterra Case Management software to support the deployment of automations for a variety of use cases.
This video focuses on the notifications, alerts, and approval requests using Slack for Bonterra Impact Management. The solutions covered in this webinar can also be deployed for Microsoft Teams.
Interested in deploying notification automations for Bonterra Impact Management? Contact us at sales@sidekicksolutionsllc.com to discuss next steps.
PHP Frameworks: I want to break free (IPC Berlin 2024)Ralf Eggert
In this presentation, we examine the challenges and limitations of relying too heavily on PHP frameworks in web development. We discuss the history of PHP and its frameworks to understand how this dependence has evolved. The focus will be on providing concrete tips and strategies to reduce reliance on these frameworks, based on real-world examples and practical considerations. The goal is to equip developers with the skills and knowledge to create more flexible and future-proof web applications. We'll explore the importance of maintaining autonomy in a rapidly changing tech landscape and how to make informed decisions in PHP development.
This talk is aimed at encouraging a more independent approach to using PHP frameworks, moving towards a more flexible and future-proof approach to PHP development.
Essentials of Automations: Optimizing FME Workflows with ParametersSafe Software
Are you looking to streamline your workflows and boost your projects’ efficiency? Do you find yourself searching for ways to add flexibility and control over your FME workflows? If so, you’re in the right place.
Join us for an insightful dive into the world of FME parameters, a critical element in optimizing workflow efficiency. This webinar marks the beginning of our three-part “Essentials of Automation” series. This first webinar is designed to equip you with the knowledge and skills to utilize parameters effectively: enhancing the flexibility, maintainability, and user control of your FME projects.
Here’s what you’ll gain:
- Essentials of FME Parameters: Understand the pivotal role of parameters, including Reader/Writer, Transformer, User, and FME Flow categories. Discover how they are the key to unlocking automation and optimization within your workflows.
- Practical Applications in FME Form: Delve into key user parameter types including choice, connections, and file URLs. Allow users to control how a workflow runs, making your workflows more reusable. Learn to import values and deliver the best user experience for your workflows while enhancing accuracy.
- Optimization Strategies in FME Flow: Explore the creation and strategic deployment of parameters in FME Flow, including the use of deployment and geometry parameters, to maximize workflow efficiency.
- Pro Tips for Success: Gain insights on parameterizing connections and leveraging new features like Conditional Visibility for clarity and simplicity.
We’ll wrap up with a glimpse into future webinars, followed by a Q&A session to address your specific questions surrounding this topic.
Don’t miss this opportunity to elevate your FME expertise and drive your projects to new heights of efficiency.
Essentials of Automations: Optimizing FME Workflows with Parameters
Wiki Powerpoint
1. This slideshow will teach you everything you want to know about combining functions via products and quotients .
2.
3.
4. Finding Restrictions What is a restriction? A restriction is a value for a variable such as ‘x’ that would make the equal zero being undefined. Example Y=(x+4)(x-5) Sub and Solve x+4=0 Sub and Solve x-5=0 x=-4 x=5 Therefore the restrictions are 4 and 5. As if either value were inputted the one side would be multiplied against zero. We know zero multiplied by anything is equal to zero.
5. Finding Domain and Range What is Domain? Domain is the set of numbers for which a function is defined in terms of its x-values. A.K.A. All possible x-values for a given function. What is Range? Range is the set of numbers for which a function is defined in terms of its y-values. A.K.A. All possible y-values for a given function. Solve an Example y= (x+4) 2 (x+6) Or y= x 3 +14x 2 +72x+96 We know that the zeroes of the function would be -4 at an order of 2 and -6, these are the x-intercepts. Furthermore if the functions were multiplied together they would have a positive leading coefficient and is a cubic function. Therefore the function is extending upward in a positive manner from 3 to 1 thus the domain is XER and YER (ER= means element of the real number system.
7. Example Four: Word Problem A movie theatre decides to gradually reduce movie ticket prices after patrons to attract more. This can be modelled by the equation P(x)= 30-0.05m with m representing the movies being played since so far this year and p representing the price of tickets. Another part of the promotion is to give away free popcorn this can be modelled in terms of z by the equation Z(x)= 4-0.02m. After creating this promotion the number of attendees can be invited by the function N(x)=10+0.3m. Write a simplified equation to show the revenue from movie ticket sales. 1. Firstly we would choose to multiply equation p by n as p represents the price of tickets and n represents the number of movie-goers. Write this out. y= n(x)p(x) y= (10+0.3m)(30-0.05m) 2. Use the FOIL method (First Outside Inside Last) to solve the equation . Y=300-0.5m+9m+0.015 3. Simplify in order of degree. Y= 9.5m+300.015
8. And now you have learned section 8.2 Products and Quotients of Functions. For more help please refer to the examples and links on our Wiki.
![Example One: Product of a Function ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)