Exam 2: Limits and Derivatives

Find the limit.

Find the limit.

If and are continuous functions with

Define the function at 0 so as to make it continuous at 0.

Select the correct Answer for each question. -Find the limit by evaluating the derivative of a suitable function at an appropriate value of x.(Hint: Use the definition of the derivative.)

Use a graph to find a number such that whenever

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

Sketch the graph of the derivative of the function whose graph is given.

Sketch the graph of the function nd evaluate

Find the limit.

If and are continuous functions with

Select the correct Answer for each question. -Let Find the value of that will make continuous on

Select the correct Answer for each question. -The cost (in dollars) of producing x units of a certain commodity is Find the average rate of change with respect to when the production level is changed from to

Find the instantaneous rate of change of the function when

Use the graph of the function to state the value of if it exists.

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

Select the correct Answer for each question. -If an equation of the tangent line to the curve at the point where is find and Select the correct Answer

Select the correct Answer for each question. -You are given that Find the limit .Select the correct Answer

Select the correct Answer for each question. -Use the graph of the function to state the value of if it exists.

If for all find Select the correct Answer