In this post, we’ll discover if calculus with analytical is a hard subject, and what studnet study in calculus with analytical geometry.

Finally, know the difference between calculus with analytical geometry and regular calculus.

## is calculus with analytical geometry hard

**Calculus with analytical geometry is not hard, it is the same as calculus 1 in difficulty. That being said all the calculus subjects that you will study in calculus 1 are the same in calculus with analytical geometry.**

to take this course you just have to be good enough in algebra 1 including the basis and foundations of function and be good at how to solve equations and inequalities. So it is not a big deal compared to what students study in college.

**what do students study in calculus with analytics?**

**1 – Trigonometry**

the second this that students learn in trigonometry is simply how to include a triangle into a circle as you can see in the image below. This method is important and very helpful to make a lot of operations.

including a triangle in a circle help students to use comfortably the cos and sin law, if you don’t know what is cos and sin you can watch this video.

Also, it will be helpful for a student taking calculus with analytic geometry to understand easily the calculus operations on these functions:

to determine the derivative of cosine or sinus you won’t be forced to memorize (what is the derivative of cos or sin), you just have to look at the circle then you can know the result.

to simplify more, this method help student to see the angle better and help to memorize some basic rules of angles student should be aware of.

So it is a very useful technic.

in trigonometry there are 3 principal functions that we use that are:

- Cosinus
- Sinus
- Tang

In calculus with analytical geometry, you will be taking these basics of geometry so you can go further and apply them in the next topics that we’re going to list below in our article.

The goal in geometry is to be able to deal with all trigonometry functions with ease. As a result to not stuck when you will need to use them with calculus advanced topics like derivatives and integrals.

In general, trigonometry is an easy subject compared to what we’re going to discover in the next paraph.

this does not offend you or make you scared but just that these subjects require a lot of work to master.

**2 – Limits and continuity**

The first thing that many people find hard in calculus with analytical geometry is limits and continuity, this is the base of calculus. Students struggle to calculate the limits of functions especially some specific functions that require memorizing some rules

As a simple definition of limits, limits are a mathematical calculation to determine how much the function is approaching a certain point.

understanding limits is very important to not prevent sticking to advanced calculus college topics.

But this subject just requires some practice then things become easy and acceptable with time.

**3 – Derivatives**

Derivatives are the second interesting topic in calculus with analytical geometry. in real life derivatives have unlimited applications such:

- determining the speed of a car or any vehicle
- calculating the revenue of a company at the specific moment
- it is also used by insurance companies that you take your insurance form, etc

a derivative is a domain that studies a change, so anything that changes or moves can be calculated by derivatives.

Derivatives require a little bit of memorization and a lot of practice. As a result, this is what makes this subject hard for many people because it requires a lot of work and repetition.

**4 – Analyzing functions**

in the analyzing functions, you will learn a lot of theorems like:

- Mean value theorem
- Extreme value theorem and critical points
- Intervals on which a function is increasing or decreasing
- Relative (local) extrema
- Sketching curves

you might find some theorems complex to digest or understand, this is noraml because they require practice and hard work

this part is concentrating on how to analyze functions using these theorems, this subject is not very tough until we get to the next hard subject.

**5 – Integrals**

Integrals are one of the hardest subjects in calculus with analytical geometry courses. It is the same as in calculus 1 there is no difference. What makes it hard is its dependency on the derivative. if you such or did not understand derivative you suffer in integrals.

if you don’t know what is integral, the integral is a math calculation technic that allows you to calculate any surface or volume of any shape or form. In the real-life integrals applications are for example :

- calculate the area of an airplane wing
- to determine the volume of an airplane tank

But in general integrals in calculus 1 or calculus with analytical geometry are not complex as in calculus 2 or 3. But in calculus1 you will learn a lot of basics about this subject.

**6 – Differential equations**

Differential equations are the domain used a lot by physicists and mechanical engineers, is a domain that allows you to study the mechanical movement of a system.

you will discover differential equations and their introductions, and you will learn some interesting topics like:

- Verifying solutions for differential equations
- Sketching slope fields
- Reasoning using slope fields
- Separation of variables
- Particular solutions to differential equations

theses subjects aren’t easy to digest they take effort to understand and require more engagement. But if you put them into the work by making a lot of exercises things will become easier and clear

## Applied calculus vs calculus with analytic geometry

**applied calculus is focusing more on practice than calculus with analytical geometry. Students in calculus with analytical geometry study theoretical aspects of calculus that are based on geometry, meaning lines curves, circles, and all aspects of trigonometry.**

while in applied calculus they are asked to know how to employ these rules in real-life problems.

applied calculus is made for students who are not interested in majoring in heavy math majors like engineering, physics, and mathematics. Most of them are taking economics, biology, life science, etc.

For example, In the applied calculus subject you will be using calculus in business like determine how the market is changing according to the sales graphs and economic evolution.

we wrote in detail an article about applied calculus, you could check it in this article.