Download Lecture8Worksheet

Lecture 8 worksheet
In this worksheet we practice writing and understanding functions.
1. What are the outputs of the following? (Some give errors.)
a. ??? is x^2
in the command window we evaluate
myfun(10);
b. ??? is x+2
in the command window we evaluate
clear
y = 3;
myfun(y)
c. ??? is x+2
in the command window we evaluate
clear
x = 3;
z = myfun(x);
d. ??? is x+2
in the command window we evaluate
clear
x = 3;
myfun(y)
e. ??? is y-10
in the command window we evaluate
myfun(5);
2. Using lookfor, find the built-in function in Matlab to determine if an integer is prime.
(Hard: Can you write a function that does this yourself?)
3. Using the function you found in the previous question, write a function primepi that
takes as input x and as output returns the number of primes that are less than or equal
to x. For example, primepi(7) should return 4, because 2,3,5,7 is a complete list of the
prime numbers less than or equal to 7.
4. Plot primepi(x) using x = 10, 20, 30, ..., 1990, 2000.
5. (Challenge: Why is plotting primepi(x) this way so slow? Can you think of a faster way
to plot the same thing? We will talk about computational complexity later.)
6. Write a function countarray.m that takes two inputs: an array A and a number a and as
output returns the number of times that a occurs in A. For example, if A is [1 2 3; 2 5 2;
1 2 6], then countarray(A,2) is 4 and countarray(A,6) is 1.
7. Recall our “funnel sequences” which all started at 1000, then randomly chose an integer
-1000 to 1000, call it x2, then randomly chose an integer -x2 to x2, and so on until
reaching 0. Write a function that takes as input an integer n and as output returns a
vector which is a funnel sequence starting at n (not starting at 1000).