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Let's go through the problems step by step.

### Problem 1:
You are asked to compute the following limit:
\[
\lim_{x \to 4} \frac{x + 3}{x - 4}
\]

#### Solution:
First, substitute \( x = 4 \) directly into the function:
\[
\frac{4 + 3}{4 - 4} = \frac{7}{0}
\]

Since the denominator approaches 0 while the numerator approaches 7, the limit tends towards infinity or negative infinity depending on the direction of the approach (from the left or the right). 

Thus:
\[
\lim_{x \to 4} \frac{x + 3}{x - 4} = \infty \text{ or } -\infty
\]
This needs to be broken down further in the next steps.

### Problem 2a:
You are asked to find:
\[
\lim_{x \to 4^+} \frac{x + 3}{x - 4}
\]

#### Solution:
As \( x \to 4^+ \) (from the right), the denominator \( x - 4 \) becomes positive but very small, while the numerator \( x + 3 \) approaches 7. Thus, the overall fraction tends to positive infinity:
\[
\lim_{x \to 4^+} \frac{x + 3}{x - 4} = +\infty
\]

### Problem 2b:
You are asked to find:
\[
\lim_{x \to 4^-} \frac{x + 3}{x - 4}
\]

#### Solution:
As \( x \to 4^- \) (from the left), the denominator \( x - 4 \) becomes negative but very small, while the numerator \( x + 3 \) still approaches 7. Thus, the overall fraction tends to negative infinity:
\[
\lim_{x \to 4^-} \frac{x + 3}{x - 4} = -\infty
\]

### Summary of Results:
1. \(\lim_{x \to 4} \frac{x + 3}{x - 4} = \infty\) (not defined, but depending on the direction, it's \( +\infty \) or \( -\infty \)).
2a. \(\lim_{x \to 4^+} \frac{x + 3}{x - 4} = +\infty\)
2b. \(\lim_{x \to 4^-} \frac{x + 3}{x - 4} = -\infty\)

Would you like more details on any part of the solution? 

Here are five related questions you might find useful:
1. What happens if the numerator also approaches zero?
2. Can limits at infinity be applied in other forms of equations?
3. How would this limit change if we added a constant to the denominator?
4. What is the difference between one-sided and two-sided limits?
5. How do we handle indeterminate forms when calculating limits?

**Tip:** Always check for one-sided limits when the denominator approaches zero, as the sign of the result can change depending on the direction of approach!

Solve the limit problems: 1) lim (x → 4) (x + 3)/(x - 4), 2a) lim (x → 4^+) (x + 3)/(x - 4), 2b) lim (x → 4^-) (x + 3)/(x - 4)

Learn how to solve limit problems involving division by zero and one-sided limits. This step-by-step solution explains how to handle limits that approach infinity, both from the left and the right, and is suitable for students in Grades 10-12.

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