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// Demonstrate the use of dynamic using System; using SystemGlobalization; class DynDemo { static void Main() { // Declare two dynamic variables dynamic str; dynamic val; // Implicit conversion to dynamic types is supported // Therefore the following assignments are legal str = "This is a string"; val = 10; ConsoleWriteLine("str contains " + str); ConsoleWriteLine("val contains " + val + '\n'); str = strToUpper(CultureInfoCurrentCulture); ConsoleWriteLine("str now contains " + str); val = val + 2; ConsoleWriteLine("val now contains " + val + '\n');

We note that both numerator and denominator tend to 0, so the quotient is indeterminate at of the form 0/0 We may therefore apply l'H pital Our limit equals ( 2/x 2 ) cos( 2/x) 2 x ( 5/x ) cos( 5/x) lim This in turn simplifies to 2 2 cos( 2/x) = 5 cos( 5/x) 5 x lim

string str2 = strToLower(CultureInfoCurrentCulture); ConsoleWriteLine("str2 contains " + str2); // Implicit conversions from dynamic types are supported int x = val * 2; ConsoleWriteLine("x contains " + x); } }

The output from the program is shown here:

To: All Students Your grade this year will be calculated based on your overall improvement I will use four measures to assess how well you understand the material All four are important Each will count toward 25 percent of your grade They are: 1 2 3 4 participation in class discussions pop quizzes tests reports

str contains This is a string val contains 10 str now contains THIS IS A STRING val now contains 12 str2 contains this is a string x contains 24

Both numerator and denominator tend to zero so the quotient is indeterminate at 0 of the form 0/0 We may apply l'H pital's Rule; differentiating numerator and denominator, we find that the limit equals lim

In the program, notice how the two variables, str and val, are declared using the dynamic type This means that type checking on actions involving these two variables will not occur at compile time As a result, any operation can be applied to them In this case, str calls the String methods, ToUpper( ) and ToLower( ), and val uses the addition and multiplication

20:

U n s a f e C o d e , P o i n t e r s , N u l l a b l e Ty p e s , D y n a m i c Ty p e s , a n d M i s c e l l a n e o u s To p i c s

operators Although these actions are compatible with the types of objects assigned to the variables in this example, the compiler has no way of knowing this It simply accepts them without question This, of course, simplifies the coding of dynamic routines, but allows the possibility that such actions will produce a runtime error In this example, the program behaves correctly at runtime because the objects assigned to these references support the actions used in the program Specifically, because val is assigned an integer value, integer operations such as addition are supported Because str is assigned a string, string operations are supported Understand, however, that it is your responsibility to ensure that all operations applied to a dynamic type are actually supported by the type of object being referred to If they aren t, a program crash will occur One other thing to notice in the preceding example: any type of object reference can be assigned to a dynamic variable This is because an implicit conversion is provided from any type to dynamic Also, a dynamic type is automatically converted to any other type Of course, if at runtime such a conversion is invalid, then a runtime error will result For example, if you add this line to the end of the preceding example,

By using some algebraic manipulations, we can reduce a variety of indeterminate limits to expressions which can be treated by l H opital s Rule We explore some of these techniques in this section

bool b = val;

This expression transforms the index passed in index into a zero-based index suitable for use on a This expression works whether lowerBound is positive, negative, or zero The ok( ) method is shown here:

// Return true if index is within bounds private bool ok(int index) { if(index >= lowerBound & index <= upperBound) return true; return false; }

x