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1 Simplify these logarithmic expressions a3 b 2 (a) ln 5 c d log2 (a3 b) (b) log3 (ab2 ) (c) ln[e 2x z3 w 2 ] (d) log10 [1000w 100] 2 Solve each of these equations for x (a) 2x 3 x = 2x e 2 2x (b) x 2x = 10x 10 3 5 (c) 22x 33x 44x = 6 5 2 (d) 2x 3x = x x 3 2 3 e 3 Calculate each of these derivatives d (a) ln[cos(x 2 )] dx x3 d ln (b) dx x 1 d cos(e x ) (c) e dx d cos(ln x) (d) dx 4 Calculate each of these integrals (a) (b) (c)

TABLE 25-2

IList defines the following properties: bool IsFixedSize { get; } bool IsReadOnly { get; } If the collection is of fixed size, IsFixedSize is true This means elements cannot be inserted or removed If the collection is read-only, then IsReadOnly is true This means the contents of the collection cannot be changed IList defines the following indexer: object this[int index] { get; set; } You will use this indexer to get or set the value of an element However, you cannot use it to add a new element to the collection To add an element to a list, call Add( ) Once it is added, you can access the element through the indexer

Be vigilant in maintaining parallel construction in your use of titles and names For instance, if you refer to the chairman of the board as Mr Jones, you should refer to everyone by their title and last name, from

The IDictionary interface defines the behavior of a non-generic collection that maps unique keys to values A key is an object that you use to retrieve a value at a later date Thus, a collection that implements IDictionary stores key/value pairs Once the pair is stored, you can retrieve it by using its key IDictionary inherits ICollection and IEnumerable The methods declared by IDictionary are summarized in Table 25-3 Several methods throw an ArgumentNullException if an attempt is made to specify a null key and null keys are not allowed To add a key/value pair to an IDictionary collection, use Add( ) Notice that the key and its value are specified separately To remove an element, specify the key of the object in a call to Remove( ) To empty the collection, call Clear( )

5 Use the technique of logarithmic differentiation to calculate the derivative of each of the following functions x2 x (a) x 3 3 x +1

Part II:

Method void Add(object key, object value) void Clear( ) bool Contains(object key) IDictionaryEnumerator GetEnumerator( ) void Remove(object key)

TABLE 25-3

Description Adds the key/value pair specified by key and value to the invoking collection Removes all key/value pairs from the invoking collection Returns true if the invoking collection contains key as a key Otherwise, returns false Returns the enumerator for the invoking collection Removes the entry whose key equals key

sin x (x 3 x) x2 (c) (x 2 + x 3 )4 (x 2 x) 3 x sin x (d) ln x (b) 6 There are 7 grams of a certain radioactive substance present at noon on January 10 and 5 grams present at noon on January 15 How much will be present on January 20 7 A petri dish has 10,000 bacteria present at 10:00 am and 17,000 present at 2:00 pm How many bacteria will there be at 3:00 pm 8 A sum of $5000 is deposited on January 1, 2005 at 4% interest, compounded continuously All interest is reinvested How much money will be in the account on January 1, 2009 9 Calculate these derivatives d 1 Cos (x e x ) (a) dx x d 1 Cot (b) dx x+1 d 1 (c) Tan [ln(x 2 + x)] dx d 1 (d) Sec tan x dx 10 Calculate each of these integrals x x dx (a) 1 + x4 x2 (b) dx 1 x6 /2 2 cos x sin x dx (c) 4 0 1 cos x dx (d) 3 + x2

You can determine whether a collection contains a specific object by calling Contains( ) with the key of the desired item GetEnumerator( ) obtains an enumerator compatible with an IDictionary collection This enumerator operates on key/value pairs IDictionary defines the following properties: