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Final Exam Prep Seminar Scheduled
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I am not ready to take registrations yet, but I want to let you know that the Final Exam Seminar will be Thursday, December 4 from 9:00 am to 6:00 pm, and will be held on the UM campus (room 100 St. Paul's College). I will send you an email
when I am ready to take registrations.
Did you read my tips on how to study and learn Math 1500? If not, here is a link to those important suggestions: These are tips for the 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: You need to study Lesson 10 (Max/Min Word Problems) and Lesson 11 (Antiderivatives and Integrals) 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: 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 this question: This question is similar to my Practise Problems 1 and 2 in Lesson 10. Note, being told that x and y are nonnegative means that x and y are both
> 0. Similar to my question 3 in Lesson 10. Don't forget to include your domain.
This question is similar to my Practise Problems 22 and 23 in Lesson 10, but even worse.
Part (a), x is the circumference of the circle so x=2pi r, allowing you to solve r in terms of x and sub into
the area of a circle to get area as a function of x, the formula for A1 that they request. Don't forget to include the domain of x.
Part (b), 1-x is the perimeter of the equilateral triangle, so each side is just 1-x divided by 3. The area of an equilateral triangle is square root of 3 times s-squared, all divided by 4, where s is the length of one side. You can then sub in to get rid of s to create your formula for A2
in terms of x. Don't forget to include the domain of x. It will be the same as for part (a).
Part (c) is pretty easy and it will still be the same domain.
Part (d) will be a mess. Note that the endpoints in your domain will prove important. One of the extremes is coming from the endpoints.
This is just standard antiderivative and indefinite integral stuff like what I am doing in my Lecture Problem 1 in Lesson 11. Simply use the Antiderivative Formulas given at the
start of the lesson. Be sure you call your final answer F(x). Distinguish between the given lower-case f and the answer, upper-case F.
This is just standard antiderivative and indefinite integral stuff like what I am doing in my Lecture Problem 2 in Lesson 11. Simply use the
Antiderivative Formulas given at the start of the lesson. Be sure you call your final answer F(x). Distinguish between the given lower-case f and the answer, upper-case F.
This question requires the method I use in Lecture Problem 13 in Lesson 11. Your question is actually more pleasant than either of my two examples. I suggest you do this question open book. Note, you can check your
answer by doing the definite integral of x dx from x=0 to x=1.
Never worry about this kind of question again. I am confident that you will not have to use this method on an exam. That's why you are welcome to do this question open-book.
This question is NOT to be solved using antiderivative formulas! You couldn't solve part (b) that way anyway. You can solve part (a) that way and you can use that answer as a check, but you
will get no credit for that method.
For part (a), you have to draw a graph of f(x) = x+3 from x=1 to x=5, then find the area between the vertical lines x=1 and x=5, below the graph of f(x) and above the x-axis using geometric methods. You should notice the shape is a trapezoid, so you can find the area by cutting it into a rectangle and triangle.
Again, in part (b) , draw the graph of f(x) = square root of (16 - x^2) from x=-4 to
x=4 and find the area between the curve and the x-axis. Hint: the graph is a semicircle.
This is just more standard antiderivative stuff like what I am doing in my Lecture Problem 1 in Lesson 11. This time they are definite
integrals. Simply use the Antiderivative Formulas given at the start of the lesson. But then sub in the given endpoints to evaluate the definite integrals.
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