Calculess

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📚 Calculus Library for JS and NPM

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# Calculess.js
A calculus library for javascript. Created by [Blake Sanie](http://www.blakesanie.com).
# Install
Download using [NPM](https://www.npmjs.com/package/calculess)
```console
$ npm install calculess
```
Download using [Yarn](https://yarnpkg.com/en/package/calculess)
```console
$ yarn add calculess
```
Embed using [jsDelivr](https://www.jsdelivr.com/package/npm/calculess)
```html
<script src="https://cdn.jsdelivr.net/npm/calculess@1.0.2/lib.js"></script>
```
# Getting Started
Import and initialize package
```javascript
var Calculess = require('calculess');
var Calc = Calculess.prototype;
```
# Documentation
## Limits
Evaluate a limit
```javascript
Calc.limAt( x , function );
```
Evaluate a limit from the left
```javascript
Calc.limLeftOf( x , function );
```
Evaluate a limit from the right
```javascript
Calc.limRightOf( x , function );
```
### Methods:
* Accept **±Infinity** as x value (parameter)
* Can output **±Infinity**
* Output **NaN** when the *limit does not exist*

### Examples:

```javascript
function recip(x) {
    return 1 / x;
}

Calc.limLeftOf(0, recip); // -Infinity
Calc.limRightOf(0, recip); // Infinity
Calc.limAt(0, recip); // NaN
Calc.limAt(1, recip); // 1
```
***
***

## Derivatives
<img src="https://www.wikihow.com/images/c/cc/Tangent_animation.gif" width="200px"></img>

Evaluate f'(x)
* Note: If the given function is not continuous or differentiable at the target, **NaN** is returned
```javascript
Calc.deriv( x , function );
```
Evaluate a derivative to the nth degree of x
* Note: as the degree increases, .nthDeriv() becomes **less accurate**. Also, continuity and differentiability are **not checked**.
```javascript
Calc.nthDeriv( degree, x , function );
```

### Examples:

```javascript
function para(x) {
    return x * x;
}

Calc.deriv(2, para); // 4
Calc.nthDeriv(2, 2, para); // 2
Calc.nthDeriv(3, 2, para); // 0

function sharp(x) {
    return Math.abs(x);
}

Calc.deriv(1, sharp); // 1
Calc.nthDeriv(2, 1, sharp); // 0
Calc.deriv(0, sharp); // NaN
```
***
***
## Integrals
<img src="https://upload.wikimedia.org/wikipedia/commons/6/61/Riemann_sum_%28rightbox%29.gif" width="200px"></img>

Evaluate an integral using midpoint [Riemann Sums](https://en.wikipedia.org/wiki/Riemann_sum)
```javascript
Calc.integral( start , end , function , numSubintervals );
```
Evaluate a function's average value
```javascript
Calc.averageValue( start , end , function , numSubintervals );
```
Note: As the number of subintervals increases, .intregral() becomes more accurate, though more time is required for calculations
### Examples:
```javascript
function sin(x) {
    return Math.sin(x);
}

Calc.integral(0, Math.PI, sin, 10); // 2.0082484079079745
Calc.integral(0, Math.PI, sin, 100); // 2.000082249070989
Calc.integral(0, Math.PI, sin, 1000); // 2.000000822467294
Calc.integral(0, Math.PI, sin, 10000); // 2.000000008224376
Calc.integral(0, Math.PI, sin, 100000); // 2.000000000081865
```
***
***

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