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5 EXAMPLE 1 We wish to compute lim x 3 32 . Because both numerator and denominator approach zero as x 2,

x 2

Once you sign in, you will see your Kindle books on the home page. You can either touch a book to start reading, or touch the Shopping Cart to start shopping in the Kindle store.

(empty)

x 8

Direction 1 causes the limit to be computed as a left-hand limit with values of x approaching a from below. Direction 1 causes the limit to be computed as a right-hand limit with values of x approaching a from above.

NOTE: Touching the Shopping Cart will start up your Safari browser. From there you can purchase Kindle books. Once you are done, you will need to exit Safari and start up the Kindle app once again.

The default for the Limit command is Direction Automatic, which provides Direction 1 except for limits at . Thus, Mathematica may give a misleading representation of the limit of a discontinuous function if the Direction option is omitted.

x 0

Fig. 2-16.

To read a Kindle book, touch on the book cover. The options for reading can be found along the bottom row of icons. You can add a bookmark by touching the plus (+) button. Once the bookmark is set, the plus (+) turns to a minus (-). You can go to the cover, table of contents, or beginning of the book (or specify any location in the book) by touching the button. The font, as well as the color of the page, can be adjusted. One very interesting feature is the ability to change the page to Black, which is great when reading at night. To advance pages, either swipe from right to left, or touch the right-hand side of the page. To go back a page, just swipe from left to right or touch the lefthand side of the page. Tap the screen and a slider appears at the bottom, which you can move to advance to any page in the book.

Limit Abs[x], x 0 x 1 By default, only the right-hand limit has been computed, since no direction was specified. To fully analyze the limit we must compute the left-hand limit as well. Limit Abs[x], x 0, Direction 1 x 1 The limit does not exist since the left- and right-hand limits are different numbers.

Limit[1/x, x 0, Direction 1] Limit[1/x, x 0, Direction 1]

Like the Kindle Reader, the Kobo Reader asks you first to sign in to your existing Kobo Books account. All of your existing Kobo Books will then be available for reading. Kobo uses a bookshelf approach, similar to iBooks. Tap the book cover for whichever book you wish to open. Or, touch the I m Reading tab to pick up with what you were reading last. You can also directly go to the Kobo store to purchase books by touching the Store tab.

The functi ons in the next example exhibit a different behavior. As x 0, the function oscillates an infinite number of times. Mathematica returns the limit as an Interval object. Interval[{min, max}] represents the range of values between min and max.

The top node represents the set of all the attributes and the bottom node the empty set. The nodes are annotated with the names of the functions that use that subset of the attributes.

Limit[Sin[1/x], x 0] Interval[{ 1, 1}] Limit[Tan[1/x], x 0] Interval[{ , }]

Along the top of the Kobo Reader are three buttons: Table of Contents, Overview, and Bookmarks. Just touch any button to advance to the particular feature desired.

1 (1+ Log[2]) 3

x 0