Read sections 2.1, 2.2, 2.3, and 2.4
of the text (Thomas/Finney).
Make sure you are able to solve all the core problems in
these sections.
Write up the following problems and hand them in:
section 2.1, page 117: 10, 18, 28, 30, 32, 38, 50, 52
section 2.2, page 129: 14, 24, 40, 42, 50, 52a, 54a
section 2.3, page 139: 12, 18, 28, 32
section 2.4, page 152: 18, 34, 42, 44, 54, 6972 (use maple).
Do the following problems in maple and hand in your
printouts. Go through the
sample worksheet for help.
Problems with Maple? Here are the
commands I used.
I've been referring to the tangent lines through the point (p,f(p)) as
an "approximation" of the graph of f near the point (p,f(p)). In the
following problems, you will get a better feeling for what I meant by this.

Consider f(x) = 1/x at the point 10. Find L, the tangent line through
(10,f(10)).
First plot both f and L on the same plot, plotting it
from x=10.1 to x=10+.1. Then plot the difference fL, plotting it
from x=10.1 to x=10+.1.
Now plot both f and L on the same plot, plotting it
from x=10.01 to x=10+.01. Then plot the difference fL, plotting it
from x=10.01 to x=10+.01.
Finally plot both f and L on the same plot, plotting it
from x=10.001 to x=10+.001. Then plot the difference fL, plotting it
from x=10.001 to x=10+.001.
Discuss what you observed as you "zoomed in".

Consider f(x) = 1/x at the point 1. Find L, the tangent line through
(1,f(1)).
First plot both f and L on the same plot, plotting it
from x=1.1 to x=1+.1. Then plot the difference fL, plotting it
from x=1.1 to x=1+.1.
Now plot both f and L on the same plot, plotting it
from x=1.01 to x=1+.01. Then plot the difference fL, plotting it
from x=1.01 to x=1+.01.
Finally plot both f and L on the same plot, plotting it
from x=1.001 to x=1+.001. Then plot the difference fL, plotting it
from x=1.001 to x=1+.001.
Discuss what you observed as you "zoomed in".

Consider f(x) = 1/x at the point .2. Find L, the tangent line through
(.2,f(.2)).
First plot both f and L on the same plot, plotting it
from x=.2.1 to x=.2+.1. Then plot the difference fL, plotting it
from x=.2.1 to x=.2+.1.
Now plot both f and L on the same plot, plotting it
from x=.2.01 to x=.2+.01. Then plot the difference fL, plotting it
from x=.2.01 to x=.2+.01.
Finally plot both f and L on the same plot, plotting it
from x=.2.001 to x=.2+.001. Then plot the difference fL, plotting it
from x=.2.001 to x=.2+.001.
Discuss what you observed as you "zoomed in".

Consider f(x) = 1/x at the point .2. Find L, the tangent line through
(.2,f(.2)).
First plot both f and L on the same plot, plotting it
from x=.2.1 to x=.2+.1. Then plot the difference fL, plotting it
from x=.2.1 to x=.2+.1.
Now plot both f and L on the same plot, plotting it
from x=.2.01 to x=.2+.01. Then plot the difference fL, plotting it
from x=.2.01 to x=.2+.01.
Finally plot both f and L on the same plot, plotting it
from x=.2.001 to x=.2+.001. Then plot the difference fL, plotting it
from x=.2.001 to x=.2+.001.
Discuss what you observed as you "zoomed in".

Now that you've studied f(x) = 1/x near the points, x = 10, 1, .2, and
.2, discuss the relations and trends you observed when studying
x=10, 1, and .2. Also discuss the relation between what you observed
for x=.2 and x=.2
Back to
Math 140