# some questions on limit and continuity

1. Create a function, f(x), and pick a point c such that the limit of f(x) as x approaches c from the right and the limit of f(x) as x approaches c from the left are equal and the function is continuous. Show the values of the limits and explain why the function is continuous. The explanation should be intuitive as well as mathematical. Include a graph of the function.

2. Create a function, f(x), and pick a point c such that the limit of f(x) as x approaches c from the right and the limit of f(x) as x approaches c from the left are equal, the function is defined at the point c but the function is not continuous at c. Show the values of the limits and explain why the function is not continuous. The explanation should be intuitive as well as mathematical. Include a graph of the function.

3. Create a function, f(x), and pick a point c such that the limit of f(x) as x approaches c from the right and the limit of f(x) as x approaches c from the left are equal, the function is not defined at the point c and the function is not continuous at c. Show the values of the limits and explain why the function is not continuous. The explanation should be intuitive as well as mathematical. Include a graph of the function.

4. Create a function, f(x), and pick a point c such that the limit of f(x) as x approaches c from the right and the limit of f(x) as x approaches c from the left are not equal in value. Explain why the limit of f(x) as x approaches c does not exist and why the function cannot be continuous.

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#### Solution Preview

1.Create a function, f(x), and pick a point c such that the limit of f(x) as x approaches c from the right and the limit of f(x) as x approaches c from the left are equal and the function is continuous. Show the values of the limits and explain why the function is continuous. The explanation should be intuitive as well as mathematical. Include a graph of the function.

Solution:

Consider the function and c = 0

Since = f(0) so function is continuous at x = 0.

Graph of is shown below:

2. Create a function, f(x), and pick a point c such that the limit of f(x) as x approaches c from the right and the limit of f(x) as x approaches c from ...

#### Solution Summary

This posting explains the concepts of limits and continuity in details by providing four examples of functions.