Răspuns:O
Explicație pas cu pas:
Ca sa arat ca o functie e continua intr-un punct , calculez limitele laterale si valoarea functiei in acel punct. Daca acestea 3 sunt egale functia e continua.daca nu, nu
a)f(x)=x²+x xo=1
Ls :x->1 x<1 limf(x)=lim(x²+x)=1²+1=1+1=2
Ld: x-.>1 x>1 limf(x)=lim(x²+x)=1²+1=1+1=2
f(1)=1²+1=1+1=2
Lx=Ld=f(1)=2 Functia e continua
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b)f(x)=x+lxl={x+x=2x x≥0
{x-x=0 x<0
Ls:x-.0 x<0 lim f(0)=lim0=0
Ld:x->0 x>0 limf(x)=2*0=0
f(0)=0+l0l=0+0=0
Ls=Ld=f(0)=0 functia e continua
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c) f(x)={x+x² x≤0
{x+sinx x>0
Ls :x->0 x<0 limf(x) =0+0²=0+0=0
Ld ; x->0 x>0 lim f(x)=0+sino=0+0=0
f(0)=0+0=0
Ls=Ld=f(0)=0
Functia e continua in 0
