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couple reach my desk I look at them If they start Dear Tom and I don t even know the company or the writer, forget it Straight into the trash They make me mad Maybe I m old fashioned, but that s how I feel Sally, a business student approaching graduation and now on a job hunt, explains that she applies for most positions online I hesitate to say Dear Mr Smith in an E-mail, but I do it I don t know Mr Smith, so I gure it s best to be more formal, rather than less formal Sally s right Even in an E-mail, usually if you don t know the person you re writing to personally, you shouldn t use his or her rst name There are exceptions, of course A new supervisor, for example, might send an E-mail saying hello to each of her employees and use each person s rst name, even before she s met them individually, to set a tone of approachability As a general rule, though, it s better to err on the side of extra formality, rather than insuf cient formality

The following output is produced:

The positive values in nums: 1 3 5 Setting nums[1] to 99 The positive values in nums after change: 1 99 3 5

guess that the F we seek is a polynomial of degree 3 What about F (x) = x 3 We calculate that F (x) = 3x 2 That does not quite work We seek x 2 for our derivative, but we get 3x 2 This result suggests adjusting our guess We instead try F (x) = x 3 /3 Then, indeed, F (x) = 3x 2 /3 = x 2 , as desired We will write F (x) = x 3 /3 + C for our antiderivative More generally, suppose that f (x) = ax 3 + bx 2 + c x + d Using the reasoning in the last paragraph, we may find fairly easily that F (x) = ax 4 /4 + bx 3 /3 + c x 2 /2 + dx + e Notice that, once again, we have thrown in an additive constant

As the output confirms, after the value in nums[1] was changed from 2 to 99, the result of rerunning the query reflects the change This is a key point that must be emphasized Each execution of a query produces its own results, which are obtained by enumerating the current contents of the data source Therefore, if the data source changes, so, too, might the results of executing a query The benefits of this approach are quite significant For example, if you are obtaining a list of pending orders for an online store, then you want each execution of your query to produce all orders, including those just entered

As the preceding examples have shown, a query involves variables whose types relate to one another These are the query variable, the range variable, and the data source Because the correspondence among these types is both important and a bit confusing at first, they merit a closer look The type of the range variable must agree with the type of the elements stored in the data source Thus, the type of the range variable is dependent upon the type of the data source In many cases, C# can infer the type of the range variable As long as the data source implements IEnumerable<T>, the type inference can be made because T describes the type

Part I:

In practice, it is useful to have a compact notation for the antiderivative What we do, instead of saying that the antiderivative of f (x) is F (x) + C, is to write f (x) dx = F (x) + C So, for example, cos x dx = sin x + C and x 3 + x dx = and e 2x dx = e 2x + C 2 x2 x4 + +C 4 2

of the elements in the data source However, if the data source implements the non-generic version of IEnumerable, then you will need to explicitly specify the type of the range variable This is done by specifying its type in the from clause For example, assuming the preceding examples, this shows how to explicitly declare n to be an int:

var posNums = from int n in nums //