https://bbhosted.cuny.edu/webapps/blackboard/content/contentWrapper.jsp?cor Blackboard Accessibility Training Queensborough Help Blackboard Resources Home 2020 Summer (SWI) MA441 2.2 The Limit of Function EXERCISES 2.2 The Limit of a Function 253) or DNE for undefined or Does Not Exist. Enter each answer as a whole number (like f(0) L(f(z)) MII(f(0)) Huzt(f()) Question Help: @video Submit Question
The Correct Answer and Explanation is:
Thanks for sharing the image, Jeniffer. Based on what I can interpret from the visual layout and structure of the exercise titled “2.2 The Limit of a Function,” it looks like you’re working with problems that ask for evaluating function values and limits using graphical or tabular information.
Let me walk you through how to approach each of the four common types of questions seen on such exercises, assuming the graph or table shows a piecewise function or plotted values:
- Evaluating f(0) This simply means finding the value of the function at z = 0. Look at the y-coordinate corresponding to z = 0. If the point is solid (closed dot), that’s your function value. If it’s an open circle, the function is not defined there, and the answer is DNE.
- Finding lim(z → 3) f(z) This is the two-sided limit. It means checking what value the function approaches as z gets close to 3 from both sides. If the left- and right-hand sides approach the same y-value, that’s your limit. If not, then the limit does not exist.
- Evaluating lim(z → 3⁻) f(z) Here, you’re only looking from the left side of z = 3. Trace the function from values slightly less than 3 and observe which y-value it approaches.
- Evaluating lim(z → 0) f(z) This is another two-sided limit. Use the same reasoning as you did for number two but centered around zero.
To sum up, always observe whether the approach from the left and the right of the given point converge to the same value. If they do, that’s your limit. If not, DNE. And to find function values like f(0), look at whether there’s a defined point directly at that x-coordinate.
