Due in recitation section.
Make sketches of the calculator screen and hand those in when
called for. Be sure to indicate the axis scales on any sketch.

1.) Use a graphing calculator or computer to determine
which viewing window gives the most appropriate representation
of the function f(x)=sqrt(9*x-x^2)
a.) [-4,4] by [-4,4]
b.) [-5,5] by [0,100]
c.) [-10,10] by [-10,40]
d.) [-2,10] by [-2,6]

2.) Determine appropriate viewing rectangle(s) for the following functions:
a.) y= x/(x^2+20)
b.) y=x^4-3*x^3
c.) f(x)=sin(x/50)
d.) y=x^2+0.1*sin(50*x)

3.) Use your calculator to help you sketch the graph of the function:
f(x) = sin(x) if x < 0, (2*x-x^2)^(1/3) if 0 <= x <= 2,
x-2 if x > 2.
Hand in the sketch.

4.) Graph the function f(x) = x^4+d*x^2+x for several values of d.
Sketch how the graph changes for various values of d.  Hand in the
sketch.

5.) Investigate the graph of y = ln(x) in the region [0,2].  What conclusion
can you draw about the values of the function at x=0 from the graph?

6.) Graph the functions y = x^(2/3) and y = (x^2)^(1/3) in a window
that includes the origin. Does the graph show that the function
is continuous at the origin?
Does your calculator graph both functions in the same way?
Why might you expect that some calculators might give incomplete
results for y = x^(2/3) in a window that includes negative values?

Most graphing calculators permit you to graph parametric curves.
Check your manual to make sure you are able to do so.

7.) Let x=2*(t^2-2) and y = t^3-2*t. Observe how x and y
increase and decrease as a function of t.  Based upon this observation
attempt to make a rough hand sketch of the curve.  Check your result
using a parametric graphing device.  Hand a sketch in.

8.) Use the graphing calculator to estimate the leftmost point on the
curve  x = t^4-2*t^2, y= 3*t-ln(t).  Use calculus to find the exact
value of that coordinate.

Most graphing devices permit the graphing of of polar curves directly.
In some cases it may be necessary to convert the equations to parametric
form first.  For example if r = f(theta), then the parametric form
would be x = r*cos(theta) = f(theta)*cos(theta);  and
y = r*sin(theta)= f(theta)*sin(theta).  Some calculators require the use of
a specific variable called t rather than theta.

9.) Graph the curve r = sin(4*theta/5) and turn in a sketch of the final
result. How many loops does the resulting rose have?

Hint 1:  to graph this in parametric form use the equations:
x = r*cos(t) = sin(4*t/5)*cos(t)
y = r*sin(t) = sin(4*t/5)*sin(t)

Hint 2:  At what value of theta will the curve finally retrace itself?
We will need that sin[4*(t+2*n*Pi)/5] = sin[4*t/5], or that (8*n*Pi/5) be an
even multiple of Pi.  This first occurs when t = 10*Pi, so we use the
range 0 < t < Pi.

10.)  Use a graphing device to estimate the y-coordinate of the highest
point on the curve r = 3*sin(2*theta).  Then use calculus to
find the exact value.