Did you read my tips on how to study and learn Math 1500?  If not, here is a link to those important suggestions:

Did you read my Tips for Assignment 1?  If not, here is a link to those important suggestions:

Did you read my Tips for Assignment 2?  If not, here is a link to those important suggestions:

Did you read my Tips for Assignment 3?  If not, here is a link to those important suggestions:

Did you read my Tips for Assignment 4?  If not, here is a link to those important suggestions:

These are tips for the fifth assignment in the Distance/Online Math 1500 course, but I strongly recommend that you do this assignment as homework even if you are taking the classroom lecture section of the course.  These assignments are very good (and challenging) practice.

Here is a link to the actual assignment, in case you don't have it:

You need to study Lesson 10 (Max/Min Word Problems)  and Lesson 11 (Antiderivatives and Integrals) from my Intro Calculus book to prepare for this assignment.

Don't have my book?  You can download a free sample of my book and audio lectures containing Lessons 1 and  2:

First, make sure you have read my previous email about finding the domain in Max/Min Word Problems.  Be sure you do state the domain as part of your answer to this question:

Finding the Domain in Max/Min Word Problems

This question is similar to my Practise Problems 1 and 2 in Lesson 10 except there is only one unknown number, x.  Note that the reciprocal of x is 1/x.

Similar to my Lesson 10, question 6.  Note that, to minimize the amount of material, you must minimize the surface area.  Don't forget to include your domain.

This question is similar to my Practise Problem 15 in Lesson 10.  I think you will find it easier to keep x and get rid of y in your problem, however.  Don't forget to include the domain.

This is just standard antiderivative and indefinite integral stuff like what I am doing in my Lecture Problem 1 in Lesson 11.  Simply use the Antiderivative Formulas given at the start of the lesson.

This question is just like my Lecture Problem 2 in Lesson 11.  Be sure you call your final answer F(x).  Distinguish between the given lower-case f and the answer, upper-case F.

This question requires the method I use in Lecture Problem 13 in Lesson 11.  Your question is actually more pleasant than either of my two examples.  I suggest you do this question open book.  Note, you can check your answer by doing the definite integral of x dx from x=0 to x=2.

This question is NOT to be solved using antiderivative formulas! You couldn't solve part (b) that way anyway.  You can solve part (a) that way and you can use that answer as a check, but you will get no credit for that method. 

For part (a), you have to draw a graph of f(x) = x+2 from x=1 to x=5, then find the area between the vertical lines x=1 and x=5, below the graph of f(x) and above the x-axis using geometric methods.  You should notice the shape is a trapezoid, so you can find the area by cutting it into a rectangle and triangle. 

Again, in part (b) , draw the graph of f(x) = square root of (9 - x^2) from x=-3 to x=3 and find the area between the curve and the x-axis.  Hint: the graph is a semicircle.

This is just more standard antiderivative stuff like what I am doing in my Lecture Problem 1 in Lesson 11.  This time they are definite integrals.  Simply use the Antiderivative Formulas given at the start of the lesson.  But then sub in the given endpoints to evaluate the definite integrals.