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November 9 Mathematics 105D Mr. Haines Calculus I 2012 Examination #
(16) I. Compute for the following:
A.
B.
C.
D..
(9) II.
A. Prove that is a point on this curve.
B. What is at the point?
C. What is the equation of the tangent line to this curve at the point?
(10) IV. Suppose that.
A.
B.
C.
(12) V. A box with a square top and bottom has a volume of 32 cubic inches. You are to do the first few steps to determine which dimensions will produce the least expensive box if the cost of the top and bottom is 2 cents per square inch and the cost of the sides is 1 cent per square inch. It may help to draw a picture the box.
A. List the variables you would use in setting up this problem and describe them.
B. What is the objective function?
C. What is the constraint equation?
D. Use the constraint equation to write the objective function as a function of one variable. You can stop here and don’t need to optimize this function!
(16) VIII. Find the following limits:
A.
B.
C.
D..
(5) IX. What is the minimum value of the expression if?
