Some useful formulas (Midterm II) Part I. Dierential equations Basics Initial value problems: use the data to determine constants of integration. Separate variables if possible. Logistic equation L y = by(L y), general solution y = ; (a = bL). 1 Keat Appl
Some useful formulas (Midterm I) Integration tricks Double angle formula: cos 2x = cos2 x sin2 x Parts: u dv = uv v du
right
Applications of integration Area between curves:
left
(top bottom) dx.
Numerical methods x [1? + 2? + . . . 2? + 1?]. 2 M2 (x)2 w
Cramer's rule is an addition m ethod for solving syste ms of e quations. His rule makes use
of determinants which are arrays of numbers or variables (called ele m ents) enclosed between two parallel vertical bars. The deter minant below has two rows and
5 o lrli o-, s
Math
Second Exam-A
135
1. (10 pts.)
Find the equation of the normal (perpendicular to tangent) line to the curve
scribed by
2r
lny*
-.1_
.)?
r,u, :
de-
g
1
at the point (2,L). Any correct equation specifying this line is acceptable.
L
()*V+