Maple: Assignment 1
1. Define the following functions:
 f(x) = x^3  x^2 + x  1 
 g(x) = sqrt(x) + 3 
 h(x) = 2*x^2  7 
Use Maple to find:
 (f + h)(x) 
 (f / h)(x) 
 f(g(x)) 
 g(f(x)) 
 ( f(x + h)  f(x) ) / h 
 ( g(x + h)  g(x) ) / h 
(make sure you simplify the answer Maple is giving).
2. Define the functions
 f(x) = x^2 
 g(x) = sqrt(x) 
Use Maple to find f(g(x)) and g(f(x)) and simplify the result. Interpret
the answer. Is Maple correct ? Can you simplify the answer more, making certain
assumptions on x ?
3. Define the function f(x) = (x^24)*x and plot the function for x
between 3 and 3. Then plot each of the following functions:
 f(x  2), f(x  1), f(x), f(x + 1), f(x + 2) 
Interpret the result. Note: You should restrict the yaxis to better see what is
happening. Use the command
plot({f(x2), f(x1), f(x), f(x+1), f(x+2)},x=3..3,y=10..10);
4. Using the same function as in the previous example, plot the following
functions:
 f(x)  2, f(x)  1, f(x), f(x) + 1, f(x) + 2 
and interpret the result. Make sure you again restrict the yaxis to be between 10 and
10, similar to the previous problem.
5. A ball is thrown straight into the air, and the distance function depending
on time is given as:
 s(t) = 1.7 + 24.5*t  4.9* t^2 
 At what time does the ball hit the ground ?
 If your friend is standing on the balcony of a house, 5.6 meters above ground, how many
chances does he have of catching the ball, and when do they occur ?
 How long does the ball stay 3 meters above the ground ?
 If you were filming the event in slow motion, where time is reduced by half, what is the
new equation of the distance function for this time frame ?
 In the slowmotion time of the previous question, when would the ball hit the ground
