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The iPad is great for watching your favorite TV shows. You can purchase TV shows from the iTunes store, and you can download sample shows from some iPad apps, like the ABC app. Just touch the TV Shows tab at the top to see the shows you have downloaded on your iPad. Scroll through your available shows and touch Play. The video controls work just like the controls when you watch a movie.

Fig. 12-5

10 8 6 4 2

The Mean Value Theorem is similar to Rolle s Theorem and does not require f to be 0 at each endpoint of the interval: Let f be continuous on the closed interval [a, b] and differentiable on the open interval (a, b). Then there exists a number, c, between a and b such that f(b) f(a) = f ' (c) (b a). f (b) f (a) If we write the conclusion of the theorem in the form = f '(c), we see that the Mean Value b a Theorem guarantees the existence of a number, c, between a and b, such that the tangent line at (c, f(c)) is parallel to the line segment connecting the endpoints of the curve. Note: Rolle s Theorem and the Mean Value Theorem guarantee the existence of at least one number c. In actuality, there may be several.

We normally think of podcasts as being audio-only broadcasts that can be downloaded through iTunes. Video podcasts are now quite prevalent and can be found on any number of sites, including many public broadcasting websites and on iTunes U, a listing of university podcasts and information found within iTunes.

EXAMPLE 14 Find the value(s), c, guaranteed by the Mean Value Theorem for the function f ( x ) =

on the interval [0, 2]. f[b] f[a] ; b a Plot[f'[x] m, {x, 0, 2}, PlotRange { 8, 8}]] f[x_]= x + Sin[2 x] a = 0; b = 2; m = ;

LCOM max(0,(8 5 5 0 max(0,(2 2 2 0 max(0,(6 6 6 0

iTunes U Story from Gary Mazo: Recently, I was browsing the iTunes U section inside the iTunes app on the iPad with my son, who was just accepted to CalTech. We were wondering about the housing situation and, lo and behold, we found a video podcast showing a tour of the CalTech dorms. We downloaded it and the podcast went right into the podcast directory for future viewing. We were able to do a complete virtual tour of the housing without flying out there from the East Coast.

We estimate the zeros of the function f '(x) m to determine the approximate locations of c. There appear to be four values: 0.3, 0.7, 1.3, and 1.7 (approximately).

FindRoot[f'[c] m, {c, {.3, .7, 1.3, 1.7}}]

Music videos are available for your iPad from a number of sources. Often, if you buy a Deluxe album from iTunes, it might include a music video or two. Music videos can also be purchased from the iTunes store, and many record companies and recording artists make them available for free on their websites. Music videos will automatically get sorted into the Music Videos section of your Videos app. Touch the Music Videos tab and start playing the video. The controls work just as they do in all other video applications.

{0.257071, 0.753319, 1.24344, 1.75836}}

Testing object-oriented software presents some new challenges. Many conventional techniques are still appropriate. For example, functional testing of objectoriented software will be no di erent from functional testing of conventional software. Test cases will be developed based on the required functionality as described in the requirement documentation. However, structural testing of object-oriented software will be very di erent. Two structural testing approaches will be covered: MM testing and function pair testing