Yes, I know that those of you in distance don't have a midterm exam, but this will be the only chance you will get to see me do a review of Lessons 1-7 in my book.  I do not revisit these lessons at the final exam seminar.

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

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 see my tips for Assignment 1? Click here.

Did you see my tips for Assignment 2? Click here.

These are tips for the first 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.  The first assignment is a great way to build and review key skills that will be helpful for this course.

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

This assignment is very challenging!  Make sure you have studied the lessons I suggest thoroughly before you begin.  You can expect to spend a ridiculous length of time doing this assignment, if you have not studied first.  Remember, it is almost a certainty that, for every hour you spend studying my lessons, that will save you at least one hour, if not more, in time spent struggling on the assignment.  You are not saving time to start working on an assignment unprepared!  You are really increasing the time you will need to do an assignment.

Study Lesson 5 (The Differentiation Rules), Lesson 6 (Implicit Differentiation), Lesson 7 (Related Rates), and Lesson 8 (Log and Exponential Derivatives) from my Intro Calculus book to prepare for this assignment.

A good runthrough of your differentiation rules as taught in Lesson 5 and Lesson 8.  Make sure you have studied both of those lessons before you attempt this question.  Very challenging derivatives.  Lots of chain rules involved. 

I warn you, you had better have done a thorough practice of Lesson 8 before attempting these questions.

That is obviously a quotient rule, but you must notice that the top is a variable raised to a variable type.  Make sure you have studied my Lesson 8, questions 1(n) to (p) before attempting this question.  Let T = the top of the function and use logarithmic differentiation to solve dT/dx or T' for your quotient rule.

These are very challenging trig limits using the principles I illustrate in Lesson 2, question 16.  Both are a matter of exploiting the sinh/h pattern.  Make sure you state right at the beginning that the limit of sinh/h as h approaches 0 = 1 (in other words state the limit I tell you to memorize on the first page of Lesson 2).  It is important you state that known limit to justify your answers.

Divide top and bottom by theta (you can do this since you are doing the same thing to top and bottom).  You can divide each term on the bottom separately by theta.  That creates a sinh/h pattern on top and a tanh/h pattern.  You should perhaps go over to the side and solve the tanh/h limit separately, then exploit the result in your problem.

Step 1: Divide top and bottom by t.  That cancels the t in front of the sine on top, and you can divide each term on the bottom individually by t to make that a little neater.

Step 2: That nicely creates a trinomial on the bottom that can be factored.  One of those factors nicely fits what you need for sinh/h, and the other factor can just be separated as the bottom of its own fraction (understood 1 on top).  That fraction's limit is trivial, just a matter of subbing in the value of t.

This is basically combining the proofs of the coefficient rule (or constant multiple rule) and the sum rule as summarized as proofs 2 and 3 on page 3 of my book and discussed in more detail in Lesson 5. 

Just solve the derivative using the a^u rule given in Lesson 8.  Note that b is just a coefficient.  Once the derivative is solved, use the fact that h'(pi) = 1 to solve b.

Classic implicit diff as taught in my Lesson 6.  But also look at the implicit diff examples in Lesson 8.

Very similar to my Lesson 8, question 2.  Note the added bonus that lne = 1.  Make sure that you have studied questions 1(n)-(p) in this lesson, too, where I first introduced the concept of Logarithmic Differentiation.

Classic related rates (Lesson 7) similar to my question 3.  The twist is that you are given dh/dt and are asked to find dV/dt. 

Also, note that the water is leaking out, so your height and volume are decreasing.  That means your rates must be listed as negative numbers!  But never include a negative sign when writing your conclusion.  The words you use will make it clear whether something is increasing or decreasing, so a negative sign is redundant.  In fact, it could be saying the opposite of what you intend.

Classic related rates (Lesson 7) similar to my Practise Problem 15. Also look at Lecture Problem 6 and Practise Problem 16 for more examples using trig and right triangles.