Question

determinati toate asimptotwle functiei:
f:R{4}->R
f(x)=2xla2- 3x
x-4​

Answer 1

Răspuns:

f(x)=(2x²-3x)/(x-4)

Asimptota oblica y=mx+n

m=limf(x)/x  cand x→±∞=

2x²-3x)/x(x-4)=lim(2x²-3x)/(x²-4x)=2

n=lim (f(x)-mx)   x→±∞=

lim[(2x²-3x)/(x-4)-2x]=lim[(2x²-3x)-2x²+8x]/(x-4)=

lim(2x²-3x-2x²+8x)/(x-4)=lim5x/(x-4)=5

Asimptota  oblica y=2x+5

Asimptota   verticala

x->4 x<4 lim (2x²-3x)/(x-4)=(2*4²-3*4)/(4-0-4)=(32-12)/(-0)=20/(-0)= -∞

x->4 x>4 lim(2x²-3x)/(x-4)=(2*4²-3*4)/(4+0-4)=(32-12)+0=+∞

x=4asimptota  la   stanga   la   -∞

si x=4 asimptota  la  dreapta   la   +∞

Explicație pas cu pas: