# Calculus Homework Help & Answers

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### What is applied calculus?

Applied calculus is a branch of mathematics that deals with the real world. This means that you will need to know not just all of the math and science concepts, but also how to apply those ideas to the real world as well. Most follow-up applied calculus courses relate directly to engineering and technology and focus on complex topics like integral equations and partial differential equations.

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### What is calculus?

Calculus is a branch of mathematics that focuses on limits, functions, derivatives and integrals. These are the building blocks of many sciences like chemistry, physics and astrophysics. On top of general math skills, Calculus requires more of an advanced understanding of algebraic formulas to make sense out of all the terminology used in classes. Many students get help with Calculus not only to understand it better, but also to improve their grade point averages for future courses in their major.

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## Math Calculus Homework Help, Assignment Questions & Answers

### How did Isaac Newton invent calculus?

The first person to describe the calculus was Isaac Newton.

Calculus is an advanced area of mathematics that uses ideas from algebra and geometry, along with a few new concepts specific only to calculus, in order to deal with change and motion. Calculus can be used for many purposes but was developed in order to solve physics problems. The central problem in Physics at the time was understanding planetary motion. Before Newton discovered calculus, no one knew how fast planets moved or how they moved. Since there were too many variables, it was impossible to understand exactly what happened when Earth's gravity pulled on other planets during their orbits. According to Newton, forces changed the velocity of any moving objects (Newton's First Law). In equation form:

Velocity = Change in Time + Initial Velocity

He found that changing velocity was the same as multiplying by the change in time (Newton's Second Law). In equation form:

Velocity change = Force / Mass x Acceleration

In order to make any of this mathematically meaningful, Newton had to create a way to measure distance and time. For this, he introduced something he called fluxions. He also created a new unit of time, which he named seconds. A second is equal to one standard orbit of Earth around the sun. The universal law of gravitation allowed Newton to determine exactly how planets moved because it described every type of force between two objects regardless of what they were or how large either object was. Since gravitational force is proportional to mass, it follows that planets with more mass were closer to the sun and slowed down more quickly as they moved in their orbits. This led Newton to a new type of equation, which he called an "integral," that could be used for different situations involving change. Integrals are much like derivatives except that the start time or starting velocity is not included when calculating them. In order to find the integral of any equation, all you have to do is follow these steps:

1) Rewrite the equation so one quantity changes based on another (differentiation); 2) Create a table with specific values for every time under consideration; 3) Substitute each value from the table into the rewritten equation; 4) Add up all of the results from step 3.

A person who specializes in calculus is called a mathematician, and you will usually hear these people referred to as "analytic" mathematicians because they prefer to work with equations that include only numbers (as opposed to algebraic forms or geometry). Analytic mathematicians like Newton are also often called differential mathematicians since they tend to focus on figuring out the derivatives of equations. The most famous example of an analytic mathematician is probably Sir Isaac Newton, though there were other excellent finders of fluxions before his time including Robert Hooke, René Descartes and Pierre de Fermat.

### What did Newton invent? What was calculus invented for? Who first thought up calculus?

Another name for calculus is "dynamics." It was invented in order to solve problems involving physical systems in which there are forces to be considered. In most cases, the causes for these forces are gravity and collisions between objects. Before Newton, no one even knew how fast planets moved or how they moved through space because of all the variables involved with gravity and orbits. The central problem in physics at that time was understanding planetary motion around Earth. Since there were so many variables, it seemed impossible to understand exactly what happened when Earth's gravity pulled on other planets during their orbits. When Isaac Newton invented calculus, he used his insight into this problem and his new way of calculating change to create a mathematical law that described every type of force between two objects of any type. Newton's law of universal gravitation explained that the force between any two objects was proportional to the product of their masses and inversely proportional to the square of their distance apart. With this one equation, Newton unified all other theories about motion at that time into a single, comprehensive body of ideas. He also invented calculus as part of his work on gravity because it allowed him to calculate things like how fast planets were moving around Earth and how long it would take each planet to complete its orbit by calculating derivatives from formulas he had created.

### What are the steps involved with creating an integral?

If you were given an integral problem that looked like this: y = 2 – x2 + 3x – 4 then these are some of the steps you would take to create an integral table:

1) Rewrite the equation so one quantity changes based on another;

2) Create a table with specific values for every time under consideration;

3) Substitute each value from the table into the rewritten equation;

4) Add up all of the results from step 3.

### Help with Integration in calculus

Integration is the opposite of differentiation, and in many ways it is the inverse process. In other words, integration involves finding areas under a curve or determining volumes of solids that represent different shapes, while differentiation mostly deals with determining speeds and accelerations based on information from curves or objects.

### Help with calculus differentiation problems

Calculus differentiation problems almost always involve determining the rate or speed of change of a function. In order to do this, you need to determine the derivative of that function. Then you can either find what is changing and how fast it's changing by using derivatives or you can figure out where changes occur based on information from a differentiable equation.

## Calculus homework help

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### What is work done in calculus?

In mathematics , specifically in calculus , work is a scalar quantity measured by the line integral of force over a distance.

The concept of work has a long history, dating back to the dawn of civilization. As early as 600 B.C., Archimedes used concepts that are similar to those underlying modern work, and reported accurate values for it [1] Mathematically, work is defined as the following: if an object does not move from its initial position and a force is exerted upon it over a period of time, then the final velocity of the object will be some function (vis viva) of the initial velocity and path (line segment) traversed . Isaac Newton expressed this exact same idea mathematically when he wrote F ds = ma . The dimensions of work are distance x force, and like power , the dimension of work is force x distance. Work can be expressed as W = F dx and its SI unit is the joule ( J ).

The concept of work was originally developed in Newtonian mechanics but it has since been generalized to a much broader range of physical situations, such as thermal physics or quantum field theory . It can also refer to any type of exertion that causes energy transfer, including friction between surfaces. [2] In all cases, work is measured by considering the path along which the "force" acts through space - which may not be straight. An example would be when lifting a book against gravity while standing on an incline.

A force of three newtons acting for one second on a 1 kg mass, which is being pulled from point A to point B.

### How is work done in calculus?

This particular question can be answered very easily by looking at the other side of the equation - F ds = ma . In this expression, we have two quantities found on both sides of the equation: F and m . It makes sense that if you increase one, you must decrease the other so that they each remain balanced. If you rearrange both sides , thus reducing each side by one variable (and changing their order), then this would result in W=F dx - using ds as distance instead of F ds = ma . The quantity F - also known as the force of a spring or other elastic object - can be calculated by using several different methods.

### How is work done used in calculus?

The concept of work has been highly useful in many different areas of science , from physics to engineering . Take for example a free body diagram you may have learned about at school. This represents the forces acting upon an object and how these forces lead to displacement . If these displacements are then studied carefully, it's possible to determine what types of forces were needed , relative magnitudes, directions, etc. In order to solve this type of problem " analytically ", one would need to use the concepts discussed above (calculus). It allows scientists [3] (as well as engineers) to determine how energy is transferred from one object to another . This, in turn, helps us better understand our surroundings.

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