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

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.

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.

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:

You need to study Lesson 2 (Limits), Lesson 3 (Continuity), Lesson 4 (The Definition of Derivative), and Lesson 5 (The Differentiation Rules) from my Intro Calculus book to prepare for this assignment.

Classic continuity question like my Lesson 3, questions 1 to 3.  Make sure you use the correct piece for f(-1), limit as x approaches -1-, and limit as x approaches -1+.  Hint, each piece will be used once, and only once.

Don't let the trig scare you.  Remember that I do a quick trig review in Lesson 1 of my book and also in Lesson 2 prior to question 16.  All of these things are just a matter of subbing in the number.  They solve themselves. 

Note that the angle -3pi/2 is rotating clockwise around the circle rather than counterclockwise (negative angles rotate in the opposite direction), so -3p/2 takes you to the same place as pi/2 on the circle.

This uses the Intermediate Value Theorem like my Lesson 3, questions 4 and 5.  First, pull everything over to the left side of the equation, and define the left hand side as your function f(x).  Make sure you formally state, "Let f(x) = ...."

Note that f(x) is not a polynomial because of the log function, but since log is a continuous function for its entire domain, you can declare f(x) is continuous. 

Then prove f(x) has at least one zero on (-1,0).  Be sure that you say "by Intermediate Value Theorem" as your justification, and make sure you state that f(x) is continuous.

These are rather challenging infinity limits like I teach in Lesson 2.

Note the e^x part of this limit is quite simple.  See my section about Graphing Exponential Functions in Lesson 9.  The rest is a standard infinity limit like my Lesson 2, questions 10 and 11.

Similar to my Lesson 2, question 12.  Include a note about square root of x^2 = |x| and explain that |x| = x if x is positive, or |x| = -x if x is negative.  Which is correct in this case?  Make sure you include this note.  You could even write it at the start of the problem, in the right column away from the limit you are evaluating.

See my Lesson 2, Practise Problem 74 for a similar example.  Again, include a note about square root of x^3 this time.  Note that the square root of x^6 is NOT x^3, it is the absolute value of x^3 or |x^3|.  Just like I discuss in part (b) above, that could be x^3 or -x^3, depending.  Make sure you write a note, perhaps right at the start of the question, saying what square root of x^6 simplifies to in this problem to justify your work.

Look at my Lesson 2, question 15 to understand the concepts here. 

Classic defintion of derivative question.  Similar to my Lesson 4, question 2(b).  Make sure you read the section on Simplifying Triple Deckers.

Classic differentiation rules practice as I teach in Lesson 5.

Classic tangent line application of derivatives.  Like my Lesson 5, question 2 and Practice Problems 75 to 82.

A function is not differentiable at some value x=a if its derivative is undefined or does not exist at x=a.

See my discussion in part (b) of Required Proof 1 written on page 3 of my book, and further discussed in Lesson 5.

Again, you must begin by saying f(x) = |x| = x if x>0 or -x if x<0.  (You can write this using piecwise function notation, like what we see written in question 1 above.)

Then, f'(x) = 1 if x>0 or -1 if x<0.  Again, this can be stated as a piecewise function for f'(x).

Now compute the limit as x approaches 0- for f'(x) and for x approaches 0+ for f'(x).  This should prove the limit as x approaches 0 for f'(x) does not exist.  That proves that f'(x) is undefined at x=0, and therefore, f(x) is not differentiable at x=0.

Your answers for f'(x) in the piecewise function should make it pretty easy to graph f'(x).