Description
1. (10 points) Write a program name hw3pr1.cpp which reads a list of doubles
terminated by end of file into a vector and prints the mean (or average) and the
standard deviation (look up the formula and tell where you got it in a
comment). Print an appropriate message if the list is empty.
2. (20 points) Use your my_cbrt_2 function from hw2pr4 to define a more
accurate cube root for all values of n using this pseudocode:
double my_cbrt_3(double n)
If n is zero return zero.
If n is negative return -my_cbrt_3(-n).
Otherwise,
set x to my_cbrt_2(n)
do this 10 times: x = (2/3)x + n/(3*x*x)
return x
Write a main which repeatedly reads a number n and prints cbrt(n),
my_cbrt_3(n), and the relative error of my_cubrt_3(n). Name your program
hw3pr2.cpp. (The relative error should be quite small.)
3. (20 points) Write the fibonacci function described in Exercise 3 at the end
of Chapter 8, and a main which reads x, y, and n, calls fibonacci to fill the
vector, and then prints the ratio of the last element of v divided by the next
to last element. For example, an input of 1 2 7 prints a ratio of 1.61538.
Fun fact: No matter what x and y are, the larger n is, the closer the ratio is
to the golden mean. Name your program hw3pr3.cpp.
OPTIONAL EXTRA CREDIT
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4. (10 points) In problem 2 the loop doesn’t need to be executed 10 times for
maximum accuracy. Write a program named hw3pr4.cpp to determine the smallest
number k such that looping k times is just as accurate as looping 10 times.
Hint: For k = 1 to 10, find the maximum relative error for n from 1/8 to 1
in steps of 1/1024. Use those 10 numbers to determine the smallest
number k such that looping k times is just as accurate as looping 10 times.
Name your program hw3pr4.cpp.
