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The general forms for these operators are shown here: value << num-bits value >> num-bits Here, value is the value being shifted by the number of bit positions specified by num-bits A left shift causes all bits within the specified value to be shifted left one position and a zero bit to be brought in on the right A right shift causes all bits to be shifted right one position In the case of a right shift on an unsigned value, a 0 is brought in on the left In the case of a right shift on a signed value, the sign bit is preserved Recall that negative numbers are represented by setting the high-order bit of an integer value to 1 Thus, if the value being shifted is negative, each right shift brings in a 1 on the left If the value is positive, each right shift brings in a 0 on the left For both left and right shifts, the bits shifted out are lost Thus, a shift is not a rotate and there is no way to retrieve a bit that has been shifted out Here is a program that graphically illustrates the effect of a left and right shift Here, an integer is given an initial value of 1, which means that its low-order bit is set Then, eight shifts are performed on the integer After each shift, the lower eight bits of the value are shown The process is then repeated, except that a 1 is put in the eighth bit position, and right shifts are performed

// Demonstrate the shift << and >> operators using System; class ShiftDemo { static void Main() { int val = 1;

Identifying numerators leads to x = ( A + B) x 2 + ( 2B + C ) x + ( A + 2C )

Part I:

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IEnumerable<T> declares the GetEnumerator( ) method as shown here: IEnumerator<T> GetEnumerator( ) It returns an enumerator of type T for the collection Thus, it returns a type-safe enumerator IEnumerator<T> has the same two methods as does the non-generic IEnumerator: MoveNext( ) and Reset( ) It also declares a generic version of the Current property, as shown here: T Current { get; } It returns a T reference to the next object Thus, the generic version of Current is type-safe There is one other difference between IEnumerator and IEnumerator<T>: IEnumerator<T> inherits the IDisposable interface, but IEnumerator does not IDisposable defines the Dispose( ) method, which is used to free unmanaged resources

In order to create the sense of urgency needed to get your target readers to take the action that you want them to take, you need to understand their needs and wants, and you need to address them with the proper level of formality Together, these two steps understanding what s likely to motivate your readers and identifying the appropriate level of

supports the non-generic version of GetEnumerator( ) IEnumerator<T> also implements the non-generic IEnumerator interface, thus supporting the non-generic versions of Current

Solving this system, we find that A = 2/5, B = 2/5, C = 1/5 So x3 x dx = + 2x 2 + x + 2 = = 2/5 dx + x+2 ( 2/5) x + ( 1/5) dx x2 + 1 2x 1 dx + 5 x2 + 1 1 dx x2 + 1

The IComparer<T> interface is the generic version of IComparer described earlier The main difference between the two is that IComparer<T> is type-safe, declaring the generic version of Compare( ) shown here: int Compare(T x, T y) This method compares x with y and returns greater than zero if x is greater than y, zero if the two objects are the same, and less than zero if x is less that y

The IEqualityComparer<T> interface is the equivalent of its non-generic relative IEqualityComparer It defines these two methods: bool Equals(T x, T y) int GetHashCode(T obj) Equals( ) must return true if x and y are equal GetHashCode( ) must return the hash code for obj If two objects compare as equal, then their hash codes must also be the same