My Midterm Exam Prep Seminar for Math 1500 is Sunday, February 22. 

Even those of you taking the course by distance (and who therefore do not have a midterm exam) should consider attending the seminar since it will be a good review of the course so-far.  It will also be the only time I will discuss Lessons 1 to 7 in my book (there is no time to discuss these again at the final exam seminar).

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 second 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:

You need to 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.

Classic implicit diff as taught in my Lesson 6.

Classic implicit diff as taught in my Lesson 6.

A very challenging higher-order derivative like I discuss in Lesson 5, question 4.  Be very careful.  Don't miss your product rules and don't lose track of your minus signs.  Be sure you take a moment to simplify f'(x) before you proceed to f''(x).  Then, simplify f''(x) before you proceed to f'''(x).

Make sure you have studied Lessons 5 and 8 in my book before you do these derivatives. 

For part (c), make sure you have studied how to do var-to-var problems as taught in Lesson 8, questions 1(n) to 1(q).  I recommend that, you rewrite it as "y=" rather than stick with "f(x)=" just like I do when solving my Lesson 8, question 2.

This is a very challenging problem.  Be sure to take a look at my Practise Problem questions 89 and 90 in Lesson 5 before attempting this question.  The key is to label the point on the curve that is also on the tangent line as (a, lna), where a is the unknown x -coordinate of the point of tangency.  You can then say the slope of the tangent is f'(a), computing the derivative and subbing in a.  But you can also find the slope using the two points formula (y2-y1 divided by x2-x1) since you have two points on the tangent line, (a, lna) and (0,1).  You can then set those two results equal to each other in order to solve a.  Once you have solved a, you are ready to state the equation of the tangent line.

Classic related rates (Lesson 7) similar to my question 2 (but even easier).

Classic related rates (Lesson 7) similar to my Practise Problem 11.