https://file.aiquickdraw.com/mathbot/file/1722397968599ihy8dasm.pdf

solve this and show me with steps how to solve it

The document contains a series of calculus and algebra problems from a mathematics final exam. Let's work through one of the problems in detail:

### Problem 1: Limits

#### (a) Find the limit: 

\[
\lim_{x \to -1} \frac{2x - 8}{3 - 5x}
\]

**Solution Steps:**

1. **Substitute the value of \( x = -1 \)** directly into the expression:
   \[
   \frac{2(-1) - 8}{3 - 5(-1)}
   \]

2. **Calculate the numerator and the denominator**:
   - Numerator: \( 2(-1) - 8 = -2 - 8 = -10 \)
   - Denominator: \( 3 - 5(-1) = 3 + 5 = 8 \)

3. **Compute the limit**:
   \[
   \frac{-10}{8} = -\frac{5}{4}
   \]

Thus, the limit is \(-\frac{5}{4}\).

Would you like to go through another problem from the document or need further explanation on this solution? Here are some other problems we could discuss:

1. Find the limits in the other parts of Problem 1.
2. Determine \( A \) and \( B \) for continuity in Problem 2.
3. Use the definition of the derivative in Problem 3.
4. Find the equation of the tangent line in Problem 4.
5. Analyze the cost and demand functions in Problem 5.
6. Differentiate the functions listed in Problem 6.
7. Solve the implicit differentiation problem in Problem 7.
8. Find absolute maxima and minima in Problem 8.

**Tip:** When solving limits, always try direct substitution first. If you get an indeterminate form like \( \frac{0}{0} \), consider factoring, using conjugates, or applying L'Hôpital's Rule.

Learn how to solve the limit: lim x -> -1 (2x - 8) / (3 - 5x) with a detailed step-by-step solution. This problem covers key calculus concepts, including limits and direct substitution. Suitable for college-level students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation