MATH 221 Midterm: MATH 221 KSU r2u97

• School: Kansas State University
• Department: Mathematics
• Course: MATH 221
• Professor: All

Document Summary

9. 5 - rational functions and partial fraction decomposition. A2 sin x , a2 + u2 tan x. 9. 7 - integrals containing quadratic polynomials (complete the square and use a trigonometric (or hyperbolic) substitution (or use the formula giving some inverse trigonometric function). 9. 8 improper integrals: de ned as limits of de nite integrals. The limit point is +/- in nity or a discontinuity of the integrand. Locus: the set of points p such that pf = e pl (f focus, l directrix, e eccentricity). 10. 4 - parabola; if the vertex at the origin: y2 = 4px , focus(p, 0), directrix x=-p. 10. 6 - hyperbola (two branches) center(0,0): x2 b2 foci(+/-c, 0), c2 = a2 a2 + y2. B2 0 < b < a (major semiaxes is a) y2 b2 foci(+/-c, 0), c2 = a2 + b2 0 b a (major semiaxes is a, a2 transverse semiaxes b) asymptotes y = b a x.