Matematika | Középiskola » Függvény képletek

n n b =n a b ( a) = a n n a *b =(ab) an/bn=(a/b)n a0=1 a =1/an -n ap/q= q a p k n k log a xy=log a x+log a y log a x/y=log a xlog a y log a xk=k*log a x log a k x =log a x/k alog b=b parabola: X2 = 2py n a ellipszis: x2 / a2 + y2 / b2 = 1 n (an)k=an*k kör: (x-u)2 + (y-v)2 = r2 am/an=am-n egyenes: Ax+By = Ax 0 +By 0 (a+b)2=a2+2ab+b2 sin2α=2sinαcosα (a+b)3=a3+3a2b+3ab2+b3 cos2α=cos2α-sin2α a2-b2=(a+b)*(a-b) tgα=2tgα/1-tg2α a3-b3=(a-b)(a2+ab+b2) a3+b3=(a+b)(a2-ab+b2) m n m+n n a *a =a a * n b = n ab hyperbola: x2 / a2 - y2 / b2 = 1 log a b=log c b/log c a log a b=c ac=b sin30°=0.5 f(x)=xn sinα/cosα=tgα f’(x)=nxn-1 sin45°=√2/2 cosα/sinα=ctgα sin60°=√3/2 [f(x)+g(x)]’ tgα*ctgα=1 =f’(x)+g’(x) cos30°=√3/2 tgα=1/ctgα cos45°=√2/2 [cf(x)]’= ctgα=1/tgα cf’x cos60°=0.5 sin2α+cos2α=1 tg30°=√3/3 f(x)=sinx sinα=cos(90°-α) f’(x)=cosx tg45°=1 cosα=sin(90°-α) tg60°=√3 f(x)=cosx tgα=ctg(90°-α) f’(x)=-sinx

ctg30°=√3 ctgα=tg(90°-α) ctg45°=1 f(x)=tgx a/b=sinα/sinβ f’(x)= 2 2 2 ctg60°=√3/3 c =a +b -2abcosχ 1/cos2x T=absinχ/2 sin(α+β)=sinα*cosβ+cosαsinβ sin(α-β)=sinα*cosβ-cosαsinβ cos(α+β)=cosα*cosβ-sinαsinβ cos(α-β)=cosα*cosβ+sinαsinβ tg(α+β)=(tgα+tgβ)/1-tgα*tgβ tg(α-β)=(tgα-tgβ)/1+tgα*tgβ a n = a n-1 + d a n = a 1 + (n1)d S n = (a 1 + a n )n / 2 a n = a n-1 * q a n = a 1 * qn-1 S n = a 1 (qn-1) / q-1 q=0 -> S n = a 1 f(x)=ctgx f’(x)= - 1/sin2x f(x)= u(x)*v(x) f’=u’*v+V1u f(x)=1/v(x) f’=-v’/v2 f(x)= u(x)/v(x) f’=u’vv’u/v2 [f(u(x))]’= f’(u)*u’(x)