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**Introduction (brief history of calculus): **

The word calculus means small pebbles that used in counting as in abacas. There is a conflict of opinion about the name of the founder of the modern calculus. Isaac Newton on is said to be the founder of modern calculus where there is another name Gottfried Leibniz, a German mathematician came up also to be a founder of the same. Calculus homework help from Assignmnets4u incorporates all these things of Calculus like **Functions, Limits and** **Continuity**. Newton ascertains the inverse relationship between the derivative and the integral that is the association between the slope of the curve and area beneath the curve. Calculus after that was used to solve almost every impasse in modern science. Newton uses modern calculus and **Vector Calculus** in geometrical problems, which are related to physical world like planetary orbits around the sun whereas Leibniz used modern calculus to evaluate graphical problems, the Leibniz theorem is very relevant in modern economics even to this day.

**Calculus homework** help based on modern Calculus used in deviating as follows-

- To calculate the slope of the tangent line of a curve at any point along its length
- To determine velocity and acceleration of an object with a given a function describing its locality, and deciding the function of the locality of the object given its velocity and acceleration.
- Arc Length, volume and surface area of solid
- Relative and absolute extrema of objects projectile, costs, profit etc.

**Type of calculus and its uses examples: **

After a brief description and introduction of calculus, let us now go deeper into the theory of calculus. **Calculus homework help** from Assignments4u will help to understand the properties and types of the modern calculus by categorizing in two parts. Modern calculus can be divided mainly into two parts that is differential and the integral. The **differential calculus** calculates the rate of change of quantity whereas the integral calculus derives the quantity where the rate of change is known.

The other parts of calculus are as follows

**Limits:**

Limits used in calculus to define continuity. In calculus, Limit is the value that a sequence or function precede towards the input or index approaches some value.

The formula of limit can be shown as

The limit of n as n approaches c equals to L.

**Differential Calculus****: **

To study the definition properties and application of a derivative function is called differential calculus. Given a point on the domain function, a derivative function studies the small-scale behavior of the function near the point. Let us take an example where a linear function is taken

Y= mx+c where y is the dependent variable and x is the independent variable

m = Δy/ Δx is the exact value of the slope of a straight line.

Derivative evaluates an exact meaning of the notion of change in input with respect to a change in output.

**Derivative:**

A derivative is defined to be the rate of change that is the amount by which a function is changing at any given point. The real number function is the slope of the tangent line at a point on a graph. The derivative is represented by dy over dx sign representing the difference in y divided by the difference in x.

As the distance between the two x points (h) moves closer to zero, therefore the slope of the line between them come closer to be a tangent.

**Integral Calculus: **

The **integral calculus** is used to determine the application, definition, and properties of two related concepts. The **integral calculus** can further be categorized in two types that are definite and indefinite integrals.

Indefinite integrals are the inverse operation to the derivative also known as antiderivative.

The positive vital sources of information a capacity and yields a number, which gives the mathematical aggregate of zones between the chart of the information and the x-pivot. The specialized meaning of the positive indispensable includes the farthest point of an entirety of zones of square shapes, called a Riemann whole

This is a definite integral function describe as ‘the integral from a to b of* f* of x with respect to x. The Leibniz notation suggests the area under the curve to be divided by an infinite number of rectangles.

Moreover, there are other fields of Calculus, such as **Multivariate Calculus **

**Application of calculus:**

In modern days, **Calculus Applications** helps in every field of applied science. Physical science, actuarial science, statistics, economics, business medicine, biology even in the field of arts the importance of calculus is non-negotiable.

In physics, calculus is used in all concept of classical mechanism and electromagnetism is associated with calculus. The mass of an object of pre-known density, the moment of inertia total energy of an object within a conservative field can be found through calculus.

Newton’s second law of motion is an example of applied calculus in physics the change of motion statement in this theorem implies derivative stating ‘The change of momentum of a body is equal to the resultant force acting on the body and is in the same direction’. The theory of electromagnetism by Maxwell and Einstein’s theory of general relativity is also stated in a form of calculus.

Calculus homework help in probability theory to determine the probability of a random variable from an assumed density function, linear approximation in linear algebra to find the ‘best fit’. In the field of medicine, calculus is used to calculate the optimal branching angle of the blood vessel to maximize blood flow.

In the field of economics calculus help to find maximum profit minimum cost by simply calculating the marginal revenue and marginal cost. Further, the input and out of firms, social welfare and development can also be calculated by calculus help. Calculus allows to find an approximate solution to equation example fixed point iteration and linear approximation. For example, Spacecraft uses a form of Euler’s method to imprecise curved courses within zero gravity environments.

Unlike basic arithmetic or finance calculus, perhaps do not have obvious application in day-to-day life but calculus helps people every day by, from computer algorithm to modeling the spread of a disease. **Pre- Calculus** helps in every field of applied and social science. From creating a search engine with the help of algorithms for making weather, model calculus supports in developing human civilization each day. In the field of social sciences, calculus helps to determine the correct wage can assist to predict future profit, inflation or any monitory imbalance. Not only even in the field of science but calculus helps in the field of graphics and modern art as well. Artists use calculus to build a three-dimensional figure in the visual art form. In architecture, calculus is a primary tool to be used.

Calculus homework help in the modern day is a unit of development that is essential in every sector of human civilization. From basic science to social sciences, calculus is compulsory. Even in the fields of arts, the contribution of calculus in non-negotiable.

As a student needs tons of focus in calculus homework and the difference between **Calculus 1 and Calculus 2** once it involves understanding the assorted parameters connected to the study of calculus, this content in assignments4u can facilitate within the in-depth data, which will be used for future functions. The simple and clear structure of this paper will help the student understanding calculus in a much simple way and generate interest and curiosity towards this subject. It is unarguably true that mastering calculus needs a lot of practice and determination but is not impossible. Assignment4u has always strived for explaining concepts to students with the note of simplicity attached to it. A simpler concept always helps to understand the subject better and make the learning easy.

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