https://file.aiquickdraw.com/mathbot/file/1726667110141xt5n182k.jpg

Do both A and B answers only no explanation needed do both left and right for both a and b

Let's work through the answers.

For **part a (a = 0)**:
1. \(\lim_{x \to 0^-} f(x)\) (left-hand limit as \(x\) approaches 0):
   - From the graph, as \(x\) approaches 0 from the left, \(f(x)\) tends toward 2.

2. \(\lim_{x \to 0^+} f(x)\) (right-hand limit as \(x\) approaches 0):
   - As \(x\) approaches 0 from the right, \(f(x)\) also tends toward 2.

3. \(\lim_{x \to 0} f(x)\) (two-sided limit as \(x\) approaches 0):
   - Since both left and right limits are equal, the limit as \(x\) approaches 0 is 2.

4. \(f(0)\) (value of the function at \(x = 0\)):
   - The graph shows that \(f(0) = 2\).

For **part b (a = 2)**:
1. \(\lim_{x \to 2^-} f(x)\) (left-hand limit as \(x\) approaches 2):
   - As \(x\) approaches 2 from the left, \(f(x)\) approaches -2.

2. \(\lim_{x \to 2^+} f(x)\) (right-hand limit as \(x\) approaches 2):
   - As \(x\) approaches 2 from the right, \(f(x)\) tends toward 2.

3. \(\lim_{x \to 2} f(x)\) (two-sided limit as \(x\) approaches 2):
   - Since the left and right limits are not equal, the two-sided limit does not exist.

4. \(f(2)\) (value of the function at \(x = 2\)):
   - The graph shows \(f(2) = 0\) (solid point at \(x = 2\)).

Let me know if you want further details!

Use the graph to find the following limits and function values for each value of a. For a = 0 and a = 2, determine the left-hand limit, right-hand limit, two-sided limit, and the function value if it exists.

Determine the left-hand and right-hand limits as well as the function values for a = 0 and a = 2 using the provided graph. Explore key concepts of limits, continuity, and how to evaluate piecewise functions.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation