https://file.aiquickdraw.com/mathbot/file/1726450541970xoodd8lc.jpg

d) \displaystyle \lim_{x \to -1^{-}}f(x) =

The image you've provided is a step function, typically known as the floor or ceiling function. The question asks for the **left-hand limit** of \( f(x) \) as \( x \to -1^{-} \), meaning we are approaching \(-1\) from the left.

Looking at the graph:

- To find \( \lim_{x \to -1^{-}} f(x) \), we focus on the values of \( f(x) \) as \( x \) approaches \(-1\) from the left.
- The value of the function just to the left of \(-1\) (such as at \( x = -1.1 \)) is around \(-2\), as indicated by the filled dot.

Thus, we conclude:

\[
\lim_{x \to -1^{-}} f(x) = -2
\]

Would you like further details or have any other questions?

Here are some follow-up questions that could expand your understanding:
1. What is the right-hand limit \( \lim_{x \to -1^{+}} f(x) \)?
2. How does the function behave around other discontinuities, such as at \( x = 1 \)?
3. Can you define what a "step function" or "piecewise function" is?
4. How does the limit change if we approach a different discontinuity point?
5. What type of function produces this kind of graph, and what are its applications?

**Tip:** When dealing with limits at discontinuities, always check if the left-hand and right-hand limits differ to determine whether the limit exists.

d) \displaystyle \lim_{x \to -1^{-}} f(x) =

Understand how to calculate the left-hand limit of a step function as x approaches -1. This problem focuses on the concept of limits and the behavior of step functions at discontinuities, with a detailed solution on evaluating \lim_{x \to -1^{-}} f(x). Suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation