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SOLUTION For clarity we set (x) = cos x, (x) = sin x The integral becomes (x) dx 1 + 2 (x)

public virtual int BinarySearch(int startIdx, int count, object v, IComparer comp)

public virtual void CopyTo(Array ar)

or, if we realize that E is skew symmetric, ie, ET = -E, then we can also write k = sgn[l ( q )] p ( q ) Ep ( q ) 3 p ( q )

public virtual void CopyTo(Array ar, int startIdx)

By what we have just learned about Tan 1 , this last integral is equal to Tan 1 (x) + C Resubstituting (x) = cos x yields that sin x dx = Tan 1 (cos x) + C 1 + cos2 x x/(1 + x 4 ) dx

24:

(719b)

Method public virtual void CopyTo(int srcIdx, Array ar, int destIdx, int count)

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Description Copies a portion of the invoking collection, beginning at srcIdx and running for count elements, to the array specified by ar, beginning at destIdx ar must be a one-dimensional array compatible with the type of the elements in the collection Wraps ar in a fixed-size ArrayList and returns the result Returns a portion of the invoking ArrayList The range returned begins at idx and runs for count elements The returned object refers to the same elements as the invoking object Returns the index of the first occurrence of v in the invoking collection Returns 1 if v is not found Inserts the elements of c into the invoking collection, starting at the index specified by startIdx Returns the index of the last occurrence of v in the invoking collection Returns 1 if v is not found Wraps ar in a read-only ArrayList and returns the result Removes count elements from the invoking collection, beginning at idx Reverses the contents of the invoking collection Reverses count elements of the invoking collection, beginning at startIdx Replaces elements within the invoking collection, beginning at startIdx, with those specified by c Sorts the collection into ascending order Sorts the collection using the specified comparison object If comp is null, the default comparison for each object is used Sorts a portion of the collection using the specified comparison object The sort begins at startIdx and runs for count elements If comp is null, the default comparison for each object is used Returns a synchronized version of the invoking ArrayList Returns an array that contains copies of the elements of the invoking object

Either of Eqs (719a and b) is the expression sought for the curvature of the cam pro le A visualization of Eq (719b) is displayed in Fig 75 In that gure, notice that k > 0 at P1, which indicates a convexity at this point Likewise, k < 0 at P2, thereby indicating a concavity at P2

SOLUTION For clarity we set (x) = x 3 , (x) = 3x 2 The integral then becomes (x) dx 1 2 (x) We know that this last integral equals Sin 1 (x) + C Resubstituting the formula for gives a nal answer of 3x 2 dx = Sin 1 (x 3 ) + C 6 1 x You Try It: Evaluate the integral x dx 1 x4

public static ArrayList FixedSize(ArrayList ar) public virtual ArrayList GetRange(int idx, int count)

public virtual int IndexOf(object v) public virtual void InsertRange(int startIdx, ICollection c) public virtual int LastIndexOf(object v) public static ArrayList ReadOnly(ArrayList ar) public virtual void RemoveRange(int idx, int count) public virtual void Reverse( ) public virtual void Reverse(int startIdx, int count) public virtual void SetRange(int startIdx, ICollection c) public virtual void Sort( ) public virtual void Sort(IComparer comp)

Displacement (a) Dwell-rise- (b) Dwell-rise-dwell(c) Dwell-risedwell (DRD) return-dwell (DRRD) return-dwell (DRDRD)

public virtual void Sort(int startIdx, int count, IComparer comp) public static ArrayList Synchronized(ArrayList list) public virtual object[ ] ToArray( )

TABLE 24-4 Several Commonly Used Methods De ned by ArrayList (continued)

The most important inverse trigonometric functions are Sin 1 , Cos 1 , and Tan 1 We say just a few words about the other three De ne Cot x to be the restriction of the cotangent function to the interval (0, ) (Fig 621) Then Cot is decreasing on that interval and takes on all real values Therefore the inverse Cot 1 : ( , ) (0, )

(d) Rise-retrunrise (RRR)

Part II:

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