Calculus IV Problem Set 1 Fall 1998 Due 8/31/98
1. [1 point] Find the value of pi correct to 30 decimal places.
2. [1 point] Find the equation of the line tangent to f(x) = e-x
sin x where x = 1.
3. [1 point] Find the value of the ugliest integral (your choice) from
problems 9-60 in the chapter 7 review.
4. [1 point] Look at the graphs of y = sin2
x and y = sin 2x. Which one is the derivative of the other?
5. [1 point] Consider the surface f(x,y) = cos 
.
The surface doesn't have just one high point, but lots of them -- describe
(in comprehensible english) the set of points where f takes on global maximum
values.
6.[1 point] You're a drop of water at the point
(
/3,0,1/2) on the
surface z = cos x cos y. Where do you end up? Describe (in some reasonably
precise way) the region from which other drops of water will tend toward
the same spot.
7. [2 points] Get Mathematica to plot
a sphere of radius 5 centered at the origin. Explain how
you did it (you might include a printed copy
of your work if you think it will help).
8. [2 points] Consider the function f(n) = 
.
Compute f(1), f(2), f(3), f(4), (at least) and describe the pattern.
9. [3 points] Do problem #70 from section 12.1.
Explain clearly what different shapes are possible depending on the values
of a and b.
10. [2 points] Find something Mathematica
can't do.