Calculus 2 : Finding Limits and One-Sided Limits

Study concepts, example questions & explanations for Calculus 2

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Example Questions

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Example Question #411 : Finding Limits And One Sided Limits

Limits of Natural Log Functions

What is the limit of the following?

Possible Answers:

Does not exist.

Correct answer:

Explanation:

Recall the graph of a natural log function.

Loosely speaking, .

Graphing the function , is as follows and it is seen that as the function approaches three from the right hand side the function values approach negative infinity. 

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Example Question #412 : Finding Limits And One Sided Limits

Which graph is a possible sketch of the function  that possesses the following characteristics?

Possible Answers:

Graph3

There does not exist such a graph.

Graph1

Graph4

Graph2

Correct answer:

Graph4

Explanation:

Since the first derivative of  approaches  from both the left and right side of , the function should decrease on both sides of .

The only graph that is decreasing throughout is .

Graph4

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