amaila3

Basic algebraic methods are fundamental mathematical techniques used to manipulate algebraic expressions and equations. They are not part of calculus but are essential prerequisites for both precalculus and calculus. These methods include solving equations, simplifying expressions, working with variables, and understanding basic algebraic properties like the distributive property and the order of operations. In precalculus, you build upon your algebraic skills to study topics like functions, trigonometry, and polynomial functions. These concepts are crucial for success in calculus, which is a branch of mathematics that deals with rates of change and accumulation, such as differentiation and integration. So, to summarize, basic algebraic methods are not part of calculus but are an integral part of both precalculus and calculus, serving as the foundation upon which more advanced mathematical concepts are built.

Certainly! The concept of definite and indefinite integrals is fundamental in mathematics and has various real-world applications. Definite integrals, as you mentioned, are used to find the "area under a curve" and play a crucial role in calculus, physics, and engineering. For instance, in physics, they help calculate quantities like displacement, velocity, and acceleration. Maxwell's electromagnetism equations, part of the field of electromagnetism, also rely on integral calculus for solving complex problems related to electric and magnetic fields. This shows the wide-reaching impact of integrals in understanding the behavior of our physical world. Regarding their discovery and use, integral calculus was developed over centuries by mathematicians like Newton and Leibniz, who independently developed the fundamental theorems of calculus. They devised these concepts to solve problems in physics and mathematics. In essence, the discovery and application of integrals are the result of centuries of mathematical development driven by the need to understand and solve real-world problems in various fields, making them indispensable tools in science and engineering today.

Certainly! Earth's yearly average temperature is determined through a global network of weather stations, satellites, and ocean buoys. Thousands of thermometers worldwide record temperatures daily, typically at fixed hours (e.g., every hour). These data points are collected, quality-checked, and averaged to calculate daily averages for various locations. These daily averages are then used to compute monthly and annual averages. International organizations like the World Meteorological Organization oversee data coordination and ensure uniform standards. Satellite measurements provide valuable information for remote areas. Ultimately, this comprehensive network allows scientists to calculate the Earth's yearly average temperature, providing vital insights into climate trends.

No doubt leaving the past is very tough but living in the past adds no good to your present or future so It's best for everyone to leave past and move forward no matter how much hard it is..........

May be you just keep your pov to yourself. If it's not contributing any good to society

I hope this explanation will help you. Differentiation is a fundamental concept in calculus. It's the process of finding the rate at which a function changes. In simpler terms, it tells you how a quantity (usually represented as a function) is changing at a specific point. Imagine you have a function that describes the position of a car over time. Differentiation would help you determine the car's speed at a particular moment. On the other hand, a derivative is the result of differentiation. When you perform differentiation on a function, you get another function called its derivative. This new function represents the rate of change of the original function. So, if you differentiate the position function of the car, you'll get a new function representing its speed. In summary, differentiation is the process of finding rates of change, while a derivative is the mathematical expression or function that represents that rate of change. Think of differentiation as the action, and a derivative as the outcome.