Векторы

A(x_1, y₁, z₁), B(x₂, y₂, z₂), ={x₂-x₁, y₂-y₁, z₂-z₁};

(a_x, a_y, a_z)={a_x, a_y, a_z}; (b_x, b_y, b_z)={b_x, b_y, b_z};

± ={a_x±b_x, a_y±b_y, a_z±b_z}; l ={la_x, la_y, la_z};

; ;

(, )= = | | | | cosa = a× b× cosa;

(, )= =a_x b_x+ a_y b_y+ a_z b_z;

=[ ], , , - правая тройка векторов.

, ; ={c_x, c_y, c_z}, c= ;

| | = c = ab sina,

= = ; c_x = a_yb_z - a_zb_y; c_y = a_zb_x - a_xb_z; c_z = a_xb_y - a_yb_x;

Логарифмы

lg (xⁿ) = n lgx; lg (xy) = lgx + lgy; lg = lgx – lgy; lnx= ; lgx= ;

(x > 0, y > 0).

e = lim _{n® ¥} =2, 718…; a^x=e^xlna; a^x = 10 ^xlga ;

Элементы анализа

(xⁿ)´ = nx^n-1; (x^-n)´ = -nx^-(n+1); (Cxⁿ)´ =Cnx^n-1; (C/xⁿ)´ = - Cn/xⁿ⁺¹;

(cosx)´ = - sinx; (sinx)´ = cosx; (cos kx)´ = - k sinkx; (sin kx)´ = kcos kx;

(U V)´ = U´ V´; (U× V)´ = U´ V + UV´; (U/V)´ = (U´ V - UV´)/V²;

(C× e^x)´ = C× e^x; (a^Cx)´ = C× a^Cx × lna; (lnx)¢ = ; y¢ _x =[f(z(х))]¢ _x=f¢ _z× z¢ _x;

= +C, (n ¹ -1); = A +C, (n ¹ -1); = ln |x| + C;

= - +C; + C; = - + C; = sinx + C;

= - cosx + C; = sinkx+C; = - coskx+C;

(A, C, k, a - const).