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]