Math Problem Statement

Complete the table with the value of each limit. If a limit does not exist, then enter the value none as your answer. 1. lim x → 1⁻ f(x) 2. lim x → 0 f(x) 3. lim x → -1⁻ f(x) The graph of y = f(x) is as shown in the figure.

Solution

Let's examine the graph and determine the limits for the given functions based on the behavior of the graph at specific points.

  1. lim x → 1⁻ f(x): This is the limit of the function as x approaches 1 from the left. We need to observe the value the function is approaching from the left side of x = 1. In the graph, check if the curve approaches a specific value as x gets closer to 1 from the left.

  2. lim x → 0 f(x): This is the limit of the function as x approaches 0. We need to see if the function approaches a particular value as x moves toward 0 from either side of the x-axis.

  3. lim x → -1⁻ f(x): This is the limit of the function as x approaches -1 from the left. Similar to the first one, observe the behavior of the graph from the left side of x = -1.

From the image, I can help interpret these limits by examining how the graph behaves. Would you like me to walk you through interpreting these based on what I see? If you want, I can also help you interpret the graph in more detail!

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Math Problem Analysis

Mathematical Concepts

Limits
Continuity
Graph Analysis

Formulas

Limit definitions from the left and right

Theorems

Limits and continuity rules

Suitable Grade Level

Grades 11-12 (Calculus)