Consider the following recurrence, defined for n a power of 4 (for the time of some algorithm): T(n) = 3 if n = 1 2T(n/4) + 4n + 1 otherwise (a) Calculate T(16) by hand. Show your work. (b) Use the tree method to solve the recurrence exactly, assuming n is a power of 4. (c) Use the formula to calculate T(1). Show your work. (d) Use the formula to calculate T(4). Show your work. (e) Use the formula to calculate T(16). Show your work. (f) Use Mathematical Induction to prove that your formula is correct in general.

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Perform the following tasks: a. create a class named testclass that holds a single private integer field and a public constructor. the only statement in the constructor is one that displays the message “constructing”. write a main()function that instantiates one object of the testclass. save the file as testclass.cpp in the chapter 08 folder. run the program and observe the results. b. write another main()function that instantiates an array of 10 testclass objects. save the file as test class array.c . run this program and observe the results.