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.

Did you see my tips for Assignment 3? Click here.

Did you see my tips for Assignment 4? 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:

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

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 the first two questions:

Very similar to my Lesson 10, Practise Problem 6.

This is just standard antiderivative and indefinite integral stuff like what I am doing in my Lecture Problem 1 in Lesson 11. 

This is just standard antiderivative and integral stuff applied to velocity and acceleration, like what I am doing in my Lecture Problem 9 in Lesson 11. Note that they are using s to represent the position of the particle, so v = s' and a = s".

This question is NOT to be solved using antiderivative formulas! You couldn't solve it that way anyway. 

First, split the problem up into two separate definite integrals using properties of antiderivatives.  You can say it is the definite integral from -5 to 5 of x - 1 minus the definite integral from -5 to 5 of the square root expression.  Don't forget to put dx at the end of each integral!

For the integral of x-1, you have to draw a graph of f(x) = x-1 from x=-5 to x=5, then find the area between the vertical lines x= -5 and x=5, between the graph of f(x) and the x-axis using geometric methods.  You should notice the shape is a couple of triangles, so you can find the area by using the area of a triangle. Remember! Area below the x-axis is negative.

For the other integral, draw the graph of f(x) = square root of (25 - x^2) from x=-5 to x=5 and find the area between the curve and the x-axis.  Hint: the graph is a semicircle.

Don't forget that the original integral is the area of the first graph subtract the area of the second graph.

Use antiderivative properties again to split this up into three separate integrals.  Note that you can factor the coefficients out of the integrals after they have been separated.  Which is to say, the definite integral of 2 g(x) dx is 2 times the definite integral of g(x) dx.

This is again exploiting the fact that a definite integral is computing the area between a curve and the x-axis (but regions below the x-axis have negative areas).  Note, since g(x) is the definite integral between 0 and x, that means g(1) is the definite integral between 0 and 1, while g(2) is the definite integral between 0 and 2, etc.

Visualize the area each value is describing and solve it using the fact the shapes are just rectangles and triangles.  Remember! Areas below the x-axis are negative.

Almost everyone is going to get this question wrong, because they won't read the graph properly. Don't be guilty of jumping to conclusions.

One way to answer this question is to observe your answers to part (a).  That should give you a pretty good idea where g is decreasing.

A more sophisticated way is to use the Fundamental Theorem of Calculus (see my Lesson 11, question 10).  Note, you have been given that g(x) is a definite integral.  You can compute g'(x) using the Fundamental Theorem.  Now that you have computed g'(x), you need to establish where g'(x) is negative (since that is where g(x) is decreasing).  The key is to establish how does g'(x) relate to the graph of f(x) you have been given.  Therefore, how can you establish where g'(x) is negative.

There are several ways you can solve this.  The easiest is probably by looking at your answers to part (a).  You can also make a sign diagram for g'(x) using the Fundamental Theorem of Calculus again.

This is classic Fundamental Theorem stuff like what I am doing in my Lecture Problem 10 in Lesson 11. 

This is just standard antiderivative and indefinite integral stuff like what I am doing in my Lecture Problem 1 in Lesson 11.   It is just a definite integral this time.

This is just area word problem applications like what I am doing in my Lecture Problems 6 to 8 in Lesson 11.