Solutions Examination 2 Calculus III
1.
Find the vector equation of the line through the points PH- 2, 4, 5L and QH3, - 1, 6 L.
SOLUTION. The equation is
r HtL = t PQ + P = t HH3, - 1, 6 L - H- 2, 4, 5LL + H- 2, 4, 5L
= t H5, - 5, 1L + H- 2, 4, 5L.
The
Solutions Examination 1 Calculus III
4n3 5
1.
Find lim
.
6n3 + 3
SOLUTION. Dividing the numerator and denominator of the fraction by n3, we get
4n 3 5
4 5 / n3 4 2
lim
= lim
=
3
3
63
n 6n + 3 n 6 + 3 /n
2.
Express 4.1570 = 4.157015701570 as a ratio of int
Final Review Calculus III
FINAL EXAMINATION WILL BE Wednesday, June 10, 12-2 IN THE CLASS ROOM
I.
ALL PREVIOUS REVIEW SHEETS
II.
Vector valued functions of a real variable
A. Components
B. Vector operations
1. Addition, Scalar Multiplication
2. Dot Produc
Review 2 Calculus III
I.
II.
III.
IV.
V.
Differential equations
A. Generating power series satisfying a differential equation
B. Recurrence relationship of coefficients
C . Generating the first several coefficients using series manipulation
Cartesian Coor
Calculus III Review I
I.
II.
III.
Sequences
A. Definition
B. Limits
1. Archimedes Axiom: 1/n ! 0
C. Relation to Limits with a Continuous Parameter
1. L'Hpital's Rule
a.
Forcing a fraction to appear by changing t ! " to 1/t ! 0+
D. Monotone Sequences
1. Bo