Essential Formulas for Calculus, Linear Algebra, and Geometry

Def.Función: Sun, Pts cut with axes, asymptotes (vertical, if the denominator vanishes, horizontal-limits cndo tends to infinity, if radical oblique-function and the divisor is greater dividend is divided), monotony ( first derivative-points is studied before and after you leave), curvature (inflection pts) (second derivative)-is studied around-if <0-decreasing-convex,> 0-grows-concave), table values . Rouche theorem-schema-sist-ed homogeneous det-range (A) = n,, comp indet-range (A) <n. Not homogeneous-incompatible-rank (A) different rank (A / B), are comp.Que before. To solve system: 1) its rank is calculated by determinantes.2) resolves the sist x metodo gauss and is studied through the scheme. Rouche theorem-Fro benius. Discussion of systems based on a parameter - A system of linear equations is consistent if and only if the rank of matrix is equal to the rank augmented matrix with independent terms. To discuss or consider a system of linear equations (practical method) The best is almost always take the expanded matrix and find the range by placing the matrix in the form escalonada.Pero particular cases where there is better alternative method. If the number of ec matches the # of unknowns, we find the determinant of the matrix of coef and if nonzero, the sist is compared and determ. If equals zero, we calculate the rank of the augmented matrix for what we put in a phased manner and compared the ranges. D (A, B) = | AB | = root of (x _{2-x 1)} 2. ...d (P, pi) = ₁+ BB ₂AB + CB ₃+ D / root of A2 + B2 + C2,, d (pi1, pi2) - | D'-D / root d A2 + B2 + C2,, d (P, r) = plane perpendicular arch pasa x P,, intersection pi r (M)-plane is removed landa,, d (P, r) = d (P, M),,, d (pi, r) - you look first if they are parallel with inner product = 0, we take a straight pto, pto-level formula. d (r, s) - is built plane, sehalla M, d (r, s) = d (p, m ) (Pes pt line).q d between cross-2rectas you take a vector of each and a pto-are put into equation det = o-plane, with the pto-d (P, pi), Atriangulo-At = 1 / 2 | u _xv |. You catch two vectors, product vectorial.Vol tetrahedron-1 / 6 | a · (b _xc) |