Exam 2: Limits and Derivatives

Select the correct Answer for each question. -Suppose the distance s (in feet) covered by a car moving along a straight road after t sec is given by the function Calculate the (instantaneous) velocity of the car when

___ 20.Match the graph of the function with the graph of its derivative.

For the function whose graph is shown, state the following.

Estimate the value of the following limit by graphing the function Round yourAnswer correct to two decimal places.

Sketch the graph of the function and evaluate

Select the correct Answer for each question. -If use the definition of derivative to find

Find the limit

You are given and a tolerance Find a number such that whenever

Select the correct Answer for each question. -Find the instantaneous rate of change of the function when Select the correct Answer

Select the correct Answer for each question. -The displacement (in feet) of a certain particle moving in a straight line is given by where t is measured in seconds.Find the average velocity over the interval Round yourAnswer to three decimal places.

Sketch the graph of the function f and evaluate

How would you define in order to make continuous at Select the correct Answer

Select the correct Answer for each question. -Find the vertical asymptotes of the function.

Find the limit.Select the correct Answer

Use the graph of to guess at the limit if it exists.Select the correct Answer

Complete the table by computing at the given values of accurate to five decimal places.Use the results to guess at the indicated limit, if it exists, to three decimal places.

Select the correct Answer for each question. -Find the limit.Select the correct Answer

Is there a number a such that exists? If so, find the value of a and the value of the limit.

Select the correct Answer for each question. -Find the interval(s) where is continuous.

Use the precise definition of a limit to prove that