(Question 5) 8 points A closed box with a square base is produced using metal for the square bases and plastic for the sides.  The material costs are $10 per square inch for metal and $2 per square inch for plastic. The volume of this box is to be 1000 in3. Draw and label a figure representing this situation. Write an equation for the total cost to produce this box. Use calculus to find the dimensions of the box that minimize the total cost. Show your analysis.

(Question 3) 12 points Suppose that

(Question 1) 15 points Evaluate the indicated integrals if  is a positive real number constant. A.

(Question 3) 6 points Suppose

(Question 10) 8 points Car 1 is heading due south from Math-town at a rate of 40 miles per hour.Car 2 is heading due west from Math-town at a rate of 55 miles per hour.  How fast is the distance between the cars increasing when Car 1 and Car 2 are 8 miles and 4 miles from Math-town, respectively?

(Question 5) 8 points  

 (Question 7) 8 points

(Question 4) 8 points Suppose k is a non-zero real number.  Evaluate the limit algebraically.  If it does not exist, explain why not.  

(Question 2) 9 points Suppose that  is continuous at and that

(Question 10) 8 points Let .  Find the smallest number