Unit 1 – Discussion Board-Calculus

The following will examine the concepts of one-sided limits, limits, limits at infinity, and continuity.

Recall that the limit is a way to talk about a function when a value in the function cannot simply be substituted. Post your response as a reply of 100–300 words, and then comment on your fellow students’ answers in the discussion forum.

Part I

Use the following definition to establish your answer to Part I:

If f(x) is defined for all values of x near c, then the limit of f as x approaches c exists, and it is equal to L if both of the following are true:

L is finite. Both the left- and right-sided limits of f equal L. Does f need to be continuous for the limit to exist?

Part II

Evaluate the cost function C(x) for the given values in a. Address the following:

What do you notice as the values get larger? Your response should help you answer question b. Could the city remove all of the toxins in its water now that it knows the limit of C(x) as x approaches 100? Discuss what percentage of the toxin you find acceptable, and find the cost of cleanup for that percentage.