True or False. In the following exercises, justify your answer with a proof or a counterexample.
A function has to be continuous at if the exists.
You can use the quotient rule to evaluate
If there is a vertical asymptote at for the function then f is undefined at the point
If does not exist, then f is undefined at the point
Using the graph, find each limit or explain why the limit does not exist.
In the following exercises, evaluate the limit algebraically or explain why the limit does not exist.
In the following exercises, use the squeeze theorem to prove the limit.
Determine the domain such that the function is continuous over its domain.
In the following exercises, determine the value of c such that the function remains continuous. Draw your resulting function to ensure it is continuous.
In the following exercises, use the precise definition of limit to prove the limit.
A ball is thrown into the air and the vertical position is given by Use the Intermediate Value Theorem to show that the ball must land on the ground sometime between 5 sec and 6 sec after the throw.
A particle moving along a line has a displacement according to the function where x is measured in meters and t is measured in seconds. Find the average velocity over the time period
From the previous exercises, estimate the instantaneous velocity at by checking the average velocity within