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
Applications of integration Area between curves:
(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
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1. (10 pts.)
Find the equation of the normal (perpendicular to tangent) line to the curve
at the point (2,L). Any correct equation specifying this line is acceptable.