*Final Review Sheet Math H162 Winter 05*

*[n] means the topic is found on acetate n.*

*These topics and
acetates, in addition to those listed for the midterm exams, might be on
the final exam.*

*No cheat sheets on the
final exam.*

*Calculators may be
used on all parts of the final exam. *

*The Final Exam is
March 14, 1:30 pm–3:18 pm in our classroom.*

*There are three items
of theory marked *** and there will be a question about one of them on the
final exam.*

*Tools*

*Radius
of convergence [97]*

*Vectors [two pages in folder 0303]*

*Examples*

* Curves
in three-dimensional space [198]*

*Calculations *

* *

*Curves in three-dimensional space [197-202]*

* *

*Arc length for parametric curves [199-202]*

* *

*Arc
length in two-dimensional space for curves given parametrically, in rectangular
coordinates, and in polar coordinates [ 122.0-123, 203-204]*

* *

*Area
in polar coordinates [124-125]*

* *

*Tangent
(velocity) and acceleration vectors for curves in three-dimensional space [205]*

* *

*Lines and planes [206-7]*

* *

*Cones and cylinders [208-215]*

* *

* *

* *

*Proofs*

* *

****A nondecreasing infinite sequence converges
if and only if it is bounded
[29-32]*

* *

****Definition of convergent series, limit of a
convergent series, and proof that a Taylor series for a function converges to
the original function for a given value of x if and only if the remainder term
for that value of x has limit zero as n
goes to infinity [4, 5, 23,
112]*

* *

****Test for convergence of p-series [49]*

* *