diff --git a/README.md b/README.md
index 8bb9c7a..2dc3b25 100644
--- a/README.md
+++ b/README.md
@@ -33,7 +33,7 @@ $$lim_{{x \to 3}} \frac{{x^2 - 9}}{{x - 3}}$$
-* **Simplified Form:** The numerator $$\large x^2 - 9$$, can be factored as (x + 3)(x - 3) ), which simplifies the expression to:
+**Simplified Form:** The numerator $$\large x^2 - 9$$, can be factored as (x + 3)(x - 3) ), which simplifies the expression to:
@@ -44,7 +44,7 @@ $$\\begin{align*}
-* [**Final Result:**]()
+[**Final Result:**]()
Substituting ( x ) with 3, we get:
@@ -52,9 +52,9 @@ $$\large 3 + 3 = 6$$
-* **Explanation:** The limit as ( x ) approaches 3 for the function $\large \frac{{x^2 - 9}}{{x - 3}}$ is 6.
+**Explanation:** The limit as ( x ) approaches 3 for the function $\large \frac{{x^2 - 9}}{{x - 3}}$ is 6.
- This is because the factor ( x - 3 ) in the denominator cancels out with the same factor in the numerator, leaving ( x + 3 ) which evaluates to 6 when ( x ) is 3.
+This is because the factor ( x - 3 ) in the denominator cancels out with the same factor in the numerator, leaving ( x + 3 ) which evaluates to 6 when ( x ) is 3.
#
@@ -64,25 +64,25 @@ $$\lim_{{x \to -7}} \frac{{49 - x^2}}{{7 + x}}$$
-* **Simplified Form:** The numerator $\large ( 49 - x^2 )$ is a difference of squares and can be factored as $\large (7 + x)(7 - x)$.
+**Simplified Form:** The numerator $\large ( 49 - x^2 )$ is a difference of squares and can be factored as $\large (7 + x)(7 - x)$.
-* **This allows us to simplify the expression by canceling out the common factor of:** $\large ( 7 + x )$ in the numerator and denominator:
+**This allows us to simplify the expression by canceling out the common factor of:** $\large ( 7 + x )$ in the numerator and denominator:
$$\large \lim_{{x \to -7}} (7 - x)
$$
-* [**Final Result:**]()
+[**Final Result:**]()
When we substitute ( x ) with -7, the expression simplifies to:
7 - (-7) = 14
-* **Explanation:** The limit of the function $(\Large \frac{{49 - x^2}}{{7 + x}} )$ as ( x ) approaches -7 is 14.
-
- This result is obtained because after canceling the common factor, we are left with ( 7 - x ), which equals 14 when ( x ) is -7.
+**Explanation:** The limit of the function $(\Large \frac{{49 - x^2}}{{7 + x}} )$ as ( x ) approaches -7 is 14.
+
+This result is obtained because after canceling the common factor, we are left with ( 7 - x ), which equals 14 when ( x ) is -7.
#
@@ -137,10 +137,8 @@ $$\frac{1}{4}$$
The limit of the function as ( x ) approaches 1 is simply $$\frac{1}{4}$$
-
#
-
### 1f) **Limit Expression:**
$$\(\lim_{{x \to 3}} \frac{{x^3 - 27}}{{x^2 - 5x + 6}}\)$$
@@ -165,7 +163,6 @@ $$\
The limit of the function as ( x ) approaches 1 is simply $$\frac{1}{4}$$
-
#
### 1g: **Limit Expression:**
@@ -186,10 +183,9 @@ $$\
\end{align*}
\$$
-
[Final Result:]()
-
- The limit of the expression is $$\frac{1}{2}$$
+
+The limit of the expression is $$\frac{1}{2}$$
#
@@ -210,7 +206,6 @@ As ( x ) increases without bound, the value of ( \frac{1}{{x^2}} ) approaches 0
#
-
### 2b) **Limit Expression:**
( $\lim_{x \to -\infty} \frac{1}{x^2}$ )
@@ -251,7 +246,6 @@ $\lim_{x \to -\infty} (2x^4 - 3x^3 + x + 6) = \infty$
Even though ( x ) is negative, the highest power term ( x^4 ) will still lead the expression to increase without bound because the even power makes it positive.
-
#
### 2e) **Limit Expression:**