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Similarly, if we retain the rst three terms in the Fourier series expansion of the displacement of the parabolic curve, the equation of Gutman s fth-order harmonic curve can be obtained

Part II:

Method public override int GetHashCode( ) public static double GetNumericValue(char ch) public static double GetNumericValue(string str, int idx) public TypeCode GetTypeCode( ) public static UnicodeCategory GetUnicodeCategory(char ch)

3 3 1/3 [ ln 2] [ln ]1/3

Freudenstein 1-3 Harmonic Curve (Freudenstein, 1960) y= hq h 27 2pq 1 6pq + sin sin b 2p 28 b 84 b h 27 2pq 1 6pq - cos 1 - cos 28 28 b b b 2ph 27 2pq 3 6pq + sin sin 28 b 2 28 b b 4p 2 h 27 2pq 9 6pq + cos cos 28 b 3 28 b b (412)

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Meaning Returns the hash code for the invoking object Returns the numeric value of ch if ch is a digit Otherwise, returns 1 Returns the numeric value of str[idx] if that character is a digit Otherwise, returns 1 Returns the TypeCode enumeration value for Char, which is TypeCodeChar Returns the UnicodeCategory enumeration value for ch UnicodeCategory is an enumeration defined by SystemGlobalization that categorizes Unicode characters Returns the UnicodeCategory enumeration value for str[idx] UnicodeCategory is an enumeration defined by SystemGlobalization that categorizes Unicode characters Returns true if ch is a control character Otherwise, returns false Returns true if str[idx] is a control character Otherwise, returns false Returns true if ch is a digit Otherwise, returns false Returns true if str[idx] is a digit Otherwise, returns false Returns true if ch is a valid UTF-32 high surrogate Otherwise, returns false Returns true if str[idx] is a valid UTF-32 high surrogate Otherwise, returns false Returns true if ch is a letter of the alphabet Otherwise, returns false Returns true if str[idx] is a letter of the alphabet Otherwise, returns false Returns true if ch is either a letter of the alphabet or a digit Otherwise, returns false Returns true if str[idx] is either a letter of the alphabet or a digit Otherwise, returns false Returns true if ch is a lowercase letter of the alphabet Otherwise, returns false Returns true if str[idx] is a lowercase letter of the alphabet Otherwise, returns false

public static UnicodeCategory GetUnicodeCategory(string str, int idx)

public static bool IsControl(char ch) public static bool IsControl(string str, int idx) public static bool IsDigit(char ch) public static bool IsDigit(string str, int idx) public static bool IsHighSurrogate(char ch) public static bool IsHighSurrogate(string str, int idx) public static bool IsLetter(char ch) public static bool IsLetter(string str, int idx) public static bool IsLetterOrDigit(char ch) public static bool IsLetterOrDigit(string str, int idx) public static bool IsLower(char ch) public static bool IsLower(string str, int idx)

y =

Now as 0 then ln hence 1/[ln ]1/3 0 We conclude that our improper integral converges and the area under the curve and above the x-axis equals 3/[ln 2]1/3

TABLE 21-9 Methods De ned by Char (continued)

21:

y =

Method public static bool IsLowSurrogate(char ch) public static bool IsLowSurrogate(string str, int idx) public static bool IsNumber(char ch) public static bool IsNumber(string str, int idx) public static bool IsPunctuation(char ch) public static bool IsPunctuation(string str, int idx) public static bool IsSeparator(char ch) public static bool IsSeparator(string str, int idx) public static bool IsSurrogate(char ch) public static bool IsSurrogate(string str, int idx) public static bool IsSurrogatePair(char high, char low) public static bool IsSurrogatePair(string str, int idx) public static bool IsSymbol(char ch) public static bool IsSymbol(string str, int idx)

Suppose that we want to calculate the integral of a continuous function f (x) over an unbounded interval of the form [A, + ) or ( , B] The theory of the integral that we learned earlier does not cover this situation, and some new concepts are needed We treat improper integrals on in nite intervals in this section, and give some applications at the end

Meaning Returns true if ch is a valid UTF-32 low surrogate Otherwise, returns false Returns true if str[idx] is a valid UTF-32 low surrogate Otherwise, returns false Returns true if ch is a number Otherwise, returns false Returns true if str[idx] is a number Otherwise, returns false

y =

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