### 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^2-4)*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 y-axis to better see what is happening. Use the command

plot({f(x-2), f(x-1), 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 y-axis 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
1. At what time does the ball hit the ground ?
2. 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 ?
3. How long does the ball stay 3 meters above the ground ?
4. 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 ?
5. In the slow-motion time of the previous question, when would the ball hit the ground