Assignment 4
.
1) Define
the function 
using the arrow notation.
Find
i)
to 15 decimal places;
ii) 
and 
;
iii) 
and 
. Is this function
increasing or decreasing at 2? Is it
concave upwards or downwards at 2?
iv) 
and 
2) Define
the function 
then have Maple
calculate s(2), 
, 
and simplify your
results.
3)
Define the function 
then respond
to the following:
i)
Find the value of 
.
ii)
Simplify the expression 
where z is a
free variable.
iii)
Plot a graph of 
.
iv) Find
all values of x such that 
.
4)
Define the functions 
and 
then do the following.
i)
Plot a graph that shows both functions 
and 
. Experiment with different values for domain and range.
ii) Estimate the coordinates of the point of intersection of these two graphs by using left mouse-button click.
iii) Use
fsolve(
) to solve the equation 
. How does the solution of this equation relate to your
answer to part (ii)?
5) Define the function 
, then do the following:
i) Plot the graph of this function on the domain [–1, 8].
ii) Modify
your plot from part (i) to include the horizontal line 
. Use this new plot to estimate the number and approximate
values for x such that 
.
iii) What single function could you graph that would give you the same information as in part (i)
iv) Use
Maple's fsolve( )
command to approximate all solutions to the equation 
.