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If count is not null, then it contains a value The second way to determine if a nullable type contains a value is to use the HasValue read-only property defined by Nullable<T> It is shown here: bool HasValue HasValue will return true if the instance on which it is called contains a value It will return false otherwise Using the HasValue property, here is the second way to determine if the nullable object count has a value:

Assuming that a nullable object contains a value, you can obtain its value by using the Value read-only property defined by Nullable<T>, which is shown here: T Value It returns the value of the nullable instance on which it is called If you try to obtain a value from a variable that is null, a SystemInvalidOperationException will be thrown It is also possible to obtain the value of a nullable instance by casting it into its underlying type The following program puts together the pieces and demonstrates the basic mechanism that handles a nullable type:

x 0

perpendicular to DM This procedure results in the modi ed cycloidal curve having a maximum acceleration about 7 percent lower than that of the basic cycloidal curve

// Demonstrate a nullable type using System; class NullableDemo { static void Main() {

Part I:

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Now, let us consider the dwell-rise-return-dwell curve, using a combination of curves to improve the high-speed action To analyze the action, we shall use the symmetrical cycloidal curve (Fig 313), although any of the high-speed shapes, such as trapezoidal and modi ed trapezoidal, introduce the same problem A dif culty arises that did not prevail in the dwell-rise-dwell action, that is, an abrupt change or dip in the acceleration curve occurs at the maximum rise point This dip is undesirable, because it produces sudden inertia loads and vibrations In Fig 313, the problem is eliminated by blending a parabolic curve to the cycloidal curve portions A modi ed total curve is produced Also, a smoother, more desirable acceleration curve is developed with lower peak accelerations An alternative solution, necessitating less mathematical work, is to employ polynomial equations as shown in Chap 4

int count = null; if(countHasValue) ConsoleWriteLine("count has this value: " + countValue); else ConsoleWriteLine("count has no value"); count = 100; if(countHasValue) ConsoleWriteLine("count has this value: " + countValue); else ConsoleWriteLine("count has no value"); } }

1 4x

The output is shown here:

Cam angel q 057b/2

count has no value count has this value: 100

A nullable object can be used in expressions that are valid for its underlying type Furthermore, it is possible to mix nullable objects and non-nullable objects within the same expression This works because of the predefined conversion that exists from the underlying type to the nullable type When non-nullable and nullable types are mixed in an operation, the outcome is a nullable value The following program illustrates the use of nullable types in expressions:

SOLUTION The expression is indeterminate of the form We put the two fractions over a common denominator to obtain e4x 1 4x x 0 4x(e4x 1) lim Notice that the numerator and denominator both tend to zero as x 0, so this is indeterminate of the form 0/0 Therefore l H pital s Rule applies and our limit equals 4e4x 4 x 0 4e4x (1 + 4x) 4 lim Again the numerator and denominator tend to zero and we apply l H pital s Rule; the limit equals 1 16e4x = x 0 16e4x (2 + 4x) 2 lim You Try It: Evaluate the limit limx 0 1 cos x 1 + 2 x2

Derive the relationship for the dwell-rise-fall-dwell cam curve shown in Fig 314 having equal maximum acceleration values Portions I and III are harmonic; portions II and IV are horizontal straight lines

// Use nullable objects in expressions using System; class NullableDemo { static void Main() { int count = null; int result = null; int incr = 10; // notice that incr is a non-nullable type // result contains null, because count is null result = count + incr; if(resultHasValue) ConsoleWriteLine("result has this value: " + resultValue); else ConsoleWriteLine("result has no value"); // Now, count is given a value and result will contain a value count = 100; result = count + incr;

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