MTH 142 Study Guide - Partial Fraction Decomposition, Antiderivative, Ratio Test
Document Summary
Natural log rules lne = 1 ln1 = 0 ln0 = undefined ln(1/a) = -lna ln(a/b) = lna - lnb ln(ab) = lna + lnb. Part 1 - if f is an antiderivative of f (f" = f) Reunite the integral as an integral in w. Trig functions sin(2x) = 2 sinx cosx cos(2x) = cos2x - sin2x. If deg deg q, use algebraic long division and use partial fractions on the remainder. If q(x) is a product of distinct linear factors, use partial fractions of the form: If q(x) has a repeated linear factor (x-c)n, use partial fractions of the form: If q(x) contains an unfactorable quadratic factor q(x), try a partial fraction of the form: Occur when trying to integrate functions whose graphs are infinite in extent, either horizontally, vertically, or both. Basically a combination of types i and ii which we handle by breaking up the interval of integration.
