Please note that my Midterm Exam Prep Seminar for Math 1500 is coming soon (Part 1 is Saturday, Feb. 22 and Part 2 is Sunday, Feb. 23).  Even if you are distance, you will find this seminar quite a helpful review of the first half of the course.  Please note that I will not discuss the topics covered in this seminar at the Final Exam Seminar in December.  For more info about the seminar, and to sign up if you wish, please click this link:

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 I sent earlier on making sign diagrams and finding range?  Here are the links:

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.

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

Note that 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.

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

This question uses definitions I don't discuss in my book but I think it is kind of obvious which graph is which here (there is one of each).  If you look at the graph I drew at the start of my Limits Lesson on page 32, x = -1 is a removable discontinuity because we could "fix" that discontinuity by filling that hole with a dot; x = 2 is a jump discontinuity because the graph jumps from one location (y = 4) to an entirely new location (y = -1); x = 4 is an infinite discontinuity because the graph is flying away to infinity or negative infinity as it approaches 4.

This question should be solved by using the Three Steps to Check Continuity I teach in Lesson 3 to prove there is a discontinuity at x = 3, as they suggest.  Then, by visualizing what the limits tell you about the graph, you should be able to identify the type of discontinuity you are dealing with.

This question is using the Intermediate Value Theorem as illustrated in Lesson 3, questions 4 and 5.

This is a classic continuity problem, as illustrated in my Lesson 3, questions 1, 2 and 3.

This is infinite limits as discussed in Lesson 2, questions 12 to 14.  Make sure you look at my Practise Problems in that lesson, too.  Especially question 74.

Make sure that, when you are computing the square root of x-squared that you include a note on the side explaining that the square root of x-squared is the absolute value of x.  Then determine if that means the absolute value of x is x or -x, as the sign of x dictates in the particular limit.

This is similar to my Lesson 2, question 15.  You must find all the values of x that cause K/0 to find the Vertical Asymptotes (i.e., look for bottom zeros), and compute the limits as x approaches both positive infinity and negative infinity to find the Horizontal Asymptotes.  Note that there can be more than one of either asymptote.

Athough they don't make it clear, the sections they are referring to in the text suggest they want you to use the Definition of Derivative to find the derivative in this problem.  Study Lesson 4 in my book to learn how to use the definition of derivative and find the equation of a tangent line.

You can check that your answer for the derivative is correct by using the differentiation rules.  You will have to simplify the derivative in order to confirm that it matches your previous answer.

Another Definition of Derivative problem as taught in Lesson 4.

You can check that your answer for the derivative is correct by using the differentiation rules.  You will have to simplify the derivative in order to confirm that it matches your previous answer.

A good run-through of the various Differentiation Rules, as taught in Lesson 5 of my book.

I show you how to solve trig limits such as this back in Lesson 2, question 16 of my book.

An alternative method could be used that exploits the trigonometric identity: