This project is ready. Updated 16 feb.
The due date for project 4 is 22 Feb

General Rules for Maple projects.

1. Your name must appear on all printed pages as Maple input.
2. Assignments must be stabled (not paper clipped).
3. Maple output can be confusing if the worksheet is not executed
from top to bottom. Make sure you to execute the the worksheet
from top to bottom before printing.
4. Some Maple programs use too big font for printing. Be sure the
font size is reasonable.
5. The student version of Maple has a "smartplot", do NOT use this.
6. Include your name in the title of any plot.

Hints:

Project 4. (This is not a group project)
Limits and sum
#A. If f:=x->sin(x)/x, then f(0); would be division by zero and maple
tells you so. Maple will find the correct limit using
limit(f(x),x=0); In general, lim x->a f(x) is limit(f(x),x=a) in maple.
#B Maple can take limits to infinity by using "infinity" (like "Pi")
limit((1+10*x^2)/(5*x^2+56*x+89),x=infinity) is 2.
#C Sum. Maple uses sum(f(i),i=0..5) to add several values in this
case f(0) + f(1) + f(2) + f(3) + f(4) + f(5). So sum(i,i=1..4) is
1+2+3+4 = 10 and sum(i^2,i=1..4) is 1+4+9+16=30.
#D Warning, maple does not understand e^x use exp(x) instead.

Making Maple output look nicer:
Try some of these:
Diff(x^3,x) = diff(x^3,x);  or 'diff(x^3,x)' = diff(x^3,x); 
Limit(f(x),x=a) = L; or 'limit(f(x),x=a)' = L;
Sum(i,i=1..4) = sum(i,i=1..4); or 'sum(i,i=1..4)' = sum(i,i=1..4);
Int(x^3,x=1..3) = int(x^3,x=1..3); or 'int(x^3,x=1..3)' = int(x^3,x=1..3);

Problems:
#1 Use maple to find the limit of #20 on page 95.
Warning, maple does not understand e^x use exp(x) instead.
#2 Use piecewise to define a function f(x) that is -1 for x<0 and 1 otherwise.
Let maple find f(0) and limit as x->0 of f. Plot f.
#3&4 Use maple to find the limits for #12 on page 134. Do parts a, c, e and g
Warning, maple does not understand e^x use exp(x) instead.
#5 Make a table of values for the function in part e above for the
x-values 10,100,1000,...1000000 (ie 10^1 to 10^6 by factors of ten).
#6 Plot y= x sin (1/x) for x=-0.1..0.1. and find the limit as x->0 with maple.
#7 Plot y= sin (1/x) for x=-0.1..0.1. and find the limit as x->0 with maple.
What is maple trying to tell you?
#8 Define f as x^n and make Maple takes the limit of the diff quotient
f(x+h)-f(x)/h as h->0.
#9 Use maple's sum function to add the integers from 1 to a billion
and the sum of the squares of the integers from 1 to billion.
#10 Do #6 on page 152, but instead of delta t of 0.2 use 0.001. Use
evalf if necessary to produce a decimal answer.
Hint: Let i=0..999 (1..1000) and use "delta t" * 1/(1+0.001*i) so t = 0.001*i.