1. Basic Structure Example: - In this example, we define a Person structure with members for name, age, and salary. We then create a Person variable and assign values to its members. - The program prompts the user to input information about a person and displays it. ```cpp include using namespace std; struct Person { string name; int age; float salary; }; int main() { Person p1; cou...
Taylor's and Maclaurin's Series with Reminder Term The Taylor series expansion for a function about is given by: The Maclaurin series is a special case of the Taylor series where . It is given by: The reminde...
Solutions to Pfaffian Differential Equations 1. By separation of variables, a Pfaffian differential equation of the form will be equivalent to the solution:
Solve the Pfaffian differential equation: by first showing the variable separability: Here [ \text{Curl } v' = (...
Image 1: 1. Evaluate the indefinite integral:
Let , then :
1. Find an approximate value of using the trapezoidal rule with 10 s...
Image 1: Title: Taylor's and Maclaurin Series with Remainder Term Cauchy's Mean Value Theorem: If and are continuous in closed interval , and differentiable in an open interval , then there exists a point such that:
or
Provided that...
ParrotPB - A WordPress Alternative for Blogging ParrotPB is an open-source blogging platform designed as a WordPress alternative, using PocketBase as a backend. It is built with SvelteKit and Skeleton UI, providing a fast and responsive user interface. It is currently used by www.ktechs.xyz and offers a variety of features for scientists, students, bloggers, tutors, and...
| Table of contents | | ------------ | | Example 1 | | Example 2 | | Example 3 | | Example 4 | | Example 5 | | Example 6 | | Example 7 | | Example 8 | | Example 9 | Definite integrals are a crucial concept in calculus that have numerous applications in physics, engine...
Partial Differential Equations 2 |Contents| |--| | Laplace's Equation| | Poisson's Equation| | The Heat Equation| |The Wave Equation| Laplace's Equation Laplace's equation is a second order partial differential equation that arises in many applications in physics and engineering. It is given by: \n...
Introduction to JavaScript for Beginners What is JavaScript? JavaScript is a text-based programming language used both on the client-side (web browsers) and server-side (web servers). It enhances the functionality and interactivity of web pages by enabling dynamic content, animations, and user interactions. Key Features: * Client-side execution: JavaScript runs directly in web brow...
Heading mermaid mindmap root((mindmap)) Origins Long history ::icon(fa fa-book) Popularisation British popular psychology author Tony Buzan Research On effectivenessand features On Automatic creation Uses Creative techniques Strategic planning Argument mapping Tools Pen and paper Mermaid Heading ```mermaid %%{init: {"pie": {"textPosition": 0.5}, "themeVariables": {"pieOuterStrokeWi...
To integrate the given function, we'll follow a similar set of steps: First, let's identify the function: \text{function } f(x) = x^2 + 7x Next, we'll determine the antiderivative: \text{antiderivative of } f(x) = \int (x^2 + 7x) \, dx = C Now, we will proceed with the integration process step by step: 1. Splitting the function into two parts: Here, we se...
question Using latex integrate 1/x^2 showing step by step solution that a grade 4 can understand Gemini Step 1: Recall the power rule of integration , where Step 2: Apply the power rule to integrate 1/x^2 Example: Step 1: Integrate 1/x^2 **Step 2: Appl...
We want to integrate with respect to . To do this, we can use the power rule for integration, which states that
where and is the constant of integration. In our case, we have (since is in the denominator, and we need to make it a positive integer for the power rule to...
Consider the function . Compute the derivative hence or otherwise determine the value of at the point To compute the derivative of , we can use the quotient rule for differentiation. The quotient rule states that for a function , the derivative is given by: f'(z) = \frac{g'(z)h(z) - g(z)h'(z)...
To find the fixed points of the given bilinear transformation , we need to solve the equation: Given that , we have: Now, let's solve this equation for : First, multiply both sides by to eliminate the fraction: Expand the right-hand side: Rearrange the eq...
Building anything with pocketbase mermaid graph LR Chain(Pocketbase) --> Blog(["`**Blogging** with a freedom smile On your face: π€`"]) Chain --> School-system(["`school management system`"]) Chain --> Anything(["`And anything you can think of fa:fa-spinner`"]) ```mermaid %%{init: { 'logLevel': 'debug', 'theme': 'base', 'gitGraph': {'rotateCommitLabel': true}} }%% gitGraph TB: commit...
Sure, I'd be happy to help you understand the Laplace transform with an example. Let's consider the function and evaluate its Laplace transform . The Laplace transform of a function is defined as: F(s) = \mathcal{L}\{f(t)\} = \int_{0}^{\infty} e^{-st}f(t) dt For our given function , the Laplace transform is: [F...
Welcome to StackEdit!
Hi! I'm your first Markdown file in StackEdit. If you want to learn about StackEdit, you can read me. If you want to play with Markdown, you can edit me. Once you have finished with me, you can create new files by opening the file explorer on the left corner of the navigation bar...
Upmath: Math Online Editor Create web articles and blog posts with equations and diagrams Upmath significantly simplifies this task by using Markdown and LaTeX. It converts Markdown syntax extended with LaTeX equations support into HTML code you can publish anywhere on the web. Markdown Definition from Wikipedia: Markdown is a lightweight markup language with plain text formatting syntax designed...
Upmath: Math Online Editor Create web articles andΒ blog posts withΒ equations andΒ diagrams Upmath significantly simplifies this task by using Markdown and LaTeX. It converts Markdown syntax extended with LaTeX equations support into HTML code you can publish anywhere on the web. 
Markdown Definition from [Wikipedia](https://en.wikipedia.org/wiki/...
According to the video, Google Plus failed despite Google's resources and previous successes for a number of reasons, including: * Google Plus was not the first attempt by Google to enter the social media space, and it wasn't unique enough to compete with established platforms like Facebook. * Google required users to have a Google Plus account to use other Google products, which alienated many us...
According to the video, the Gucci family history is filled with fights, lawsuits, and even murder. Guccio Gucci founded the brand in 1921. The business was passed down to his sons Aldo, Rodolfo, and Vasco. The Gucci brothers helped the company grow internationally. However, there were many disagreements among the family members about how to run the company. Rodolfo never gave his son Maurizio any...
According to the video, the history of Pepsi can be summarized as follows: The video starts with Caleb Bradham, the founder of Pepsi, who created a beverage very similar to Coca-Cola but focused on health aspects. Pepsi was named after the digestive enzyme pepsin. In 1898, Caleb Bradham officially changed the name of his product to Pepsi-Cola. The video then covers the challenges Pepsi faced throu...
According to the video, Andrew Carnegie was a complex figure. He was both a ruthless businessman and a philanthropist. The video starts by acknowledging that Andrew Carnegie was the richest man in the world. But it also says that there are two sides to his story. On the one hand, he was a hypocrite who preached about workers' rights while exploiting his own workers. His actions resulted in many de...
According to the video, the key points are as follows: * The Youtuber John, who runs the channel MagnatesMedia, received three copyright strikes from another Youtuber Alex Edson. These strikes would result in the deletion of John's channel. * The reason for the strikes was that John allegedly used a few seconds of footage similar to what Alex Edson used in one of his videos. John claims that the f...
According to the video, the key points are the following: * Domino's founder Tom Monaghan had a rough childhood bouncing around foster homes and orphanages. * After a series of odd jobs, Tom bought a small failing pizza business and decided to turn it around. * Domino's success came from a focus on efficiency and innovation. They offered a limited menu, which allowed them to focus on making a bett...
According to the video, the key points are: * Starbucks started as a small retailer that sold coffee beans. * Howard Schultz, the former CEO of Starbucks, played a critical role in transforming Starbucks from a retailer to a coffee shop where people could gather and enjoy drinks. * Schultz believed that the coffee shop experience should be about more than just the coffee itself. He wanted to creat...
According to the video, Sam Zemurray was a man who built a gigantic business empire from scratch. The video talks about his journey from being an immigrant with no money to becoming the Banana King. Sam emigrated from Russia to the United States at a young age. He started working for his uncle in a grocery store. He noticed that ripe bananas were being thrown away and decided to buy them himself a...
According to the video, the history of Nintendo, a gaming company, can be summarized as follows: The video starts with how Nintendo got its start. The founder, Fusajiro Yamauchi, began by making hand-painted playing cards in 1889. Originally, Nintendo focused on producing these cards for the Yakuza, a Japanese mafia group. Nintendoβs playing cards were popular because they were high-quality and...
According to the video, Zoom was not the leading video conferencing platform before it emerged. Skype was the dominant player in the market. The video explains that Eric Yuan, the founder of Zoom, was inspired to create a better video conferencing solution after facing challenges with long distance relationships himself. When Zoom entered the market, it focused on providing a user-friendly video c...