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Update README.md #1293

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51 changes: 23 additions & 28 deletions README.md
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Expand Up @@ -262,41 +262,58 @@ $\lim_{x \to -\infty} (2x^4 - 3x^3 + x + 6) = \infty$

Even though ( x ) is negative, y.


#

## These processes above demonstrates how limits help us understand the behavior of functions near points that might not be defined, by finding equivalent expressions that are easier to evaluate.
## [3.Calculate the Following Limits]()

<br>
### 3a: Finding the limit of a polynomial function as x approaches infinity

###### <p align="center"> [Copyright 2024 Quantum Software Development. Code released under the MIT License license.](https://github.com/Quantum-Software-Development/Math/blob/3bf8270ca09d3848f2bf22f9ac89368e52a2fb66/LICENSE)
The given function is a polynomial function of the form:

$$f(x)=axn+bxn−1+cxn−2+...+dx+e$$

<br>

As x approaches infinity, the highest power of x in the function dominates the value of the function. This means that we can ignore all the lower-order terms, and simply consider the behavior of the highest-order term.
In this case, the highest-order term is 2x4. As x approaches infinity, x4 also approaches infinity, and so the function f(x) also approaches infinity.

Therefore, the limit of the function as x approaches infinity is infinity. We can write this mathematically as:

$$x→∞lim x32x4−3x3+x+6 =0$$

#

### 3b:Finding the limit of a rational function as x approaches infinity


The given function is a rational function of the form

$$f(x)=cxm+fxm−1+...+gx+haxn+bxn−1+...+dx+e$$

<br>

, where n > m. As x approaches infinity, the highest power of x in the numerator dominates the value of the numerator, and the highest power of x in the denominator dominates the value of the denominator. This means that we can ignore all the lower-order terms, and simply consider the behavior of the highest-order terms.

In this case, the highest-order term in the numerator is 2x4, and the highest-order term in the denominator is x3.

As x approaches infinity, 2x4 grows much faster than x3, and so the function f(x) approaches zero.

#

### These processes above demonstrates how limits help us understand the behavior of functions near points that might not be defined, by finding equivalent expressions that are easier to evaluate.

#

###### <p align="center"> [Copyright 2024 Quantum Software Development. Code released under the MIT License license.](https://github.com/Quantum-Software-Development/Math/blob/3bf8270ca09d3848f2bf22f9ac89368e52a2fb66/LICENSE)













Expand All @@ -310,47 +327,25 @@ Even though ( x ) is negative, y.



<!--
<br><br>

## 3.Calculate the Following Limits

### 3a: Finding the limit of a polynomial function as x approaches infinity

The given function is a polynomial function of the form:

<br>

$$f(x)=axn+bxn−1+cxn−2+...+dx+e$$

As x approaches infinity, the highest power of x in the function dominates the value of the function. This means that we can ignore all the lower-order terms, and simply consider the behavior of the highest-order term.
In this case, the highest-order term is 2x4. As x approaches infinity, x4 also approaches infinity, and so the function f(x) also approaches infinity.

Therefore, the limit of the function as x approaches infinity is infinity. We can write this mathematically as:

<br>

$$x→∞lim x32x4−3x3+x+6 =0$$

#

### 3b:Finding the limit of a rational function as x approaches infinity

<br>

The given function is a rational function of the form

<br>

$$f(x)=cxm+fxm−1+...+gx+haxn+bxn−1+...+dx+e$$

<br>

, where n > m. As x approaches infinity, the highest power of x in the numerator dominates the value of the numerator, and the highest power of x in the denominator dominates the value of the denominator. This means that we can ignore all the lower-order terms, and simply consider the behavior of the highest-order terms.

In this case, the highest-order term in the numerator is 2x4, and the highest-order term in the denominator is x3.

As x approaches infinity, 2x4 grows much faster than x3, and so the function f(x) approaches zero.



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