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12 changes: 6 additions & 6 deletions README.md
Original file line number Diff line number Diff line change
Expand Up @@ -13,7 +13,7 @@

## 1. Find the limits:

#### 1a) $$\(\lim_{x \to 3}\frac{x^{2}-9}{x-3}\)$$
### 1a) $$\(\lim_{x \to 3}\frac{x^{2}-9}{x-3}\)$$

<p align="center"> To solve this limit, we can use factorization:

Expand All @@ -33,7 +33,7 @@ $$\\begin{align*}

#

#### 1b) $$\(\lim_{x \to -7}\frac{49-x^{2}}{7+x}\)$$
### 1b) $$\(\lim_{x \to -7}\frac{49-x^{2}}{7+x}\)$$

Again, we can use factorization:

Expand All @@ -49,7 +49,7 @@ Result: The limit of the expression is -14.

#

#### 1c) $$\lim_{{x \to 0}} \frac{x^3}{2x^2 - x}$$
### 1c) $$\lim_{{x \to 0}} \frac{x^3}{2x^2 - x}$$

We factor out ( x ) from the denominator:

Expand All @@ -63,7 +63,7 @@ Result: The limit of the expression is 0.

#

#### 1d) $$f(x) = \lim_{x \to 1} \frac{x^2 - 4x + 3}{x - 1}$$
### 1d) $$f(x) = \lim_{x \to 1} \frac{x^2 - 4x + 3}{x - 1}$$

To calculate the limit, we can simplify the expression by factoring the numerator, which results in:

Expand All @@ -85,7 +85,7 @@ Result: The limit of the expression is -2.

#

#### 1e) $$\lim_{{x \to 1}} \frac{{x^2 - 2x + 1}}{{x - 1}}$$
### 1e) $$\lim_{{x \to 1}} \frac{{x^2 - 2x + 1}}{{x - 1}}$$


To calculate the limit, we can simplify the expression by factoring the numerator, which is a perfect square trinomial. Factoring (x^2 - 2x + 1), we get ((x - 1)(x - 1)). The denominator is already in factored form as (x - 1). Thus, the function simplifies to:
Expand All @@ -104,7 +104,7 @@ Result: The limit of the function as ( x ) approaches 1 is simply 0.

#

#### 1f) $$\lim_{{x \to 2}} \frac{{x - 2}}{{x^2 - 4}}$$
### 1f) $$\lim_{{x \to 2}} \frac{{x - 2}}{{x^2 - 4}}$$

To solve this limit, we need to factor the denominator and simplify the expression. The denominator ( x^2 - 4 ) can be factored into ( (x + 2)(x - 2) ), which allows us to cancel out the ( x - 2 ) term in the numerator:

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