diff --git a/calculus_lesson_1.md b/calculus_lesson_1.md
index 4d11f6b..af6089c 100644
--- a/calculus_lesson_1.md
+++ b/calculus_lesson_1.md
@@ -48,12 +48,10 @@ $\lim_{x \to a} f(x) = L$ if and only if $\lim_{x \to a^-} f(x) = \lim_{x \to a^
 
 ## Example: A Piecewise Function
 
-Consider:
-$$g(x) = 
-\begin{cases} 
-x^2, & \text{if } x < 1 \\
-3x-1, & \text{if } x \geq 1 
-\end{cases}$$
+Consider the function g(x) defined as:
+
+$$g(x) = x^2 \text{ for } x < 1$$
+$$g(x) = 3x-1 \text{ for } x \geq 1$$
 
 Let's find $\lim_{x \to 1} g(x)$:
 
@@ -67,7 +65,7 @@ Since the left and right limits are different (1 ≠ 2), $\lim_{x \to 1} g(x)$ d
 Limits don't exist when:
 1. Left and right limits are different (as in our example above)
 2. The function oscillates infinitely at the point (like $\sin(1/x)$ as x approaches 0)
-3. The function grows without bound (like $1/x^2$ as x approaches 0)
+3. The function grows without bound (like $\frac{1}{x^2}$ as x approaches 0)
 
 ## Basic Limit Laws