Did you read my tips on how to do well in Math 1500 Distance. If not, here is a link to those important suggestions:
Even if you are not taking the distance course, I think it is very useful for all Math 1500 students to attempt these hand-in assignments. In general, the assignments can be quite demanding and really force you to solidify your math skills.
You should thoroughly study Lesson 10: Max/Min Word Problems and Lesson 11: Antiderivatives (Integrals) before attempting this lesson.
Make sure you have read my earlier email about finding the domain in word problems. Here is a link to that email:
Question 1 is similar to my Practise Problem 1 in
Lesson 10 except you have only one positive number and its reciprocal. Don't forget to include the domain of x (assuming you use x as
your variable in the derivative you eventually compute).
Question 2 is very similar to my Lecture Problem 3
in Lesson 10. Don't forget to include the domain of x (assuming you
use x as your variable in the derivative you eventually compute).
Question 3
is very complicated and messy. It is similar to my Practise Problems
22 and 23. Note though that x is the perimeter of the circle and 1-x is the perimeter of the square, so the actual sides of the square are (1-x)/4 (making the
problem even messier, in my opinion). Also note that the domain of x in
parts (a), (b) and (c) will all be the same.
Question 4 is just standard antiderivative and indefinite integral stuff like what I am doing in my Lecture Problem 1 in Lesson 11.
Question 5 is just like my Lecture Problem 2 in Lesson 11.
Question 6 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.
Question 7 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. You have to draw a graph of f(x) = x+1 from x=0 to x=4 in part (a), then find the area between the vertical lines x=0 and
x=4, 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 (4 - x^2) from x=-2 to x=2 and
find the area between the curve and the x-axis. Hint: the graph is a
semicircle.
Question 8 is back to just standard definite
integral stuff like I do in the latter part of Lecture Problem 1 of
Lesson 11. (It is the Fundamental Theorem of Calculus that allows us to
solve integrals by antiderivative formulas.)
