https://file.aiquickdraw.com/mathbot/file/1727085927518zhnytrc3.jpg

The problem is asking for the conditions that define the left-hand limit of a function \( f(x) \) as \( x \) approaches \( a \).

The correct way to fill in the blanks is:

"We say \( \lim_{{x \to a^-}} f(x) = L \) if **\( f(x) \) approaches \( L \)** as **\( x \) approaches \( a \)** with **\( x < a \)**."

Thus, the answers are:
1. \( f(x) \) approaches \( L \)
2. \( x \) approaches \( a \)
3. \( x < a \)

Would you like more details on the concept of one-sided limits or any further clarification? Here are five related questions:

1. What is the right-hand limit, and how is it defined?
2. How do you determine if a two-sided limit exists?
3. What are some examples of functions with undefined limits at certain points?
4. Can a function have different left-hand and right-hand limits at the same point?
5. What is the relationship between limits and continuity?

**Tip**: One-sided limits are often used to understand behavior at points of discontinuity or in piecewise functions!

We say lim(x → a⁻) f(x) = L if [blank1] as [blank2] with [blank3].

Learn how to evaluate left-hand limits of a function with step-by-step explanations. This problem focuses on the conditions for left-hand limits, suitable for Grades 11-12 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