MAC-2312 Chapter 3: Study Guide 102 (Areas Bounded by Two Polar Curves (Example 1))

10. (10 points) Find the area of the region that lies inside the curve r = 4 cos θ and outside the curve r 2. (router )2 (rinnw) de a Ja 2

5 points) In class we spoke about numerical data and non- numerical data. Please give an mple of each and explain a method that would be best for describing the data to others les g2 (4 points) Telephone numbers in North America consist of 10 digits (including the area de). How many different telephone numbers are possible, given that the first digit cannot a 0 or 1? 7. (4 pts each) A jar contains seven differently colored balls. If we remove 5 balls, one at a time: a) How many color sequences are possible? ) How many color combinations are possible? 8. (4 pts each) An experiment consists of rolling a die one time. a) List all the elements in the sample space.

Compute an approximation to integral 1 2 1/x dx, which gives the area under y = 1/x for 1 x 2, using a modified Riemann sum with the (NOT equally spaced) partition 1,1.1, l.l2, l.l3, l.l4, l.l5, l.l6, l.l7,2 and left hand endpoints EXCEPT neglecting the area of the last rectangle. This amounts to computing the sum of the areas of the rectangles as shown in the following fig As you can see in the figure, the area of the last rectangle is relatively small compared to the others, and the other rectangles already give an overestimate of the area. Please note that the problem is NOT asking for the value of integral 1 2 1/x dx. Rather it is asking for the EXACT values of the areas of the 7 approximating rectangles and for the EXACT value of the sum of the areas of the rectangles. Calculator approximations (no matter how accurate) will NOT be accepted. Do the calculations by hand using fractions (until you notice the pattern in the areas). The area of the first rectangle = The area of the second rectangle = The area of the third rectangle = The area of the fourth rectangle = The area of the fifth rectangle = The area of the sixth rectangle = The area of the seventh rectangle = The sum of the areas of the 7 rectangles =