[tex]\text{Studiem continuitatea func\c tiei f \^in }x_0=0\\\lim\limits_{{x\rightarrow0},x<0}f(x)=\lim\limits_{x\rightarrow0,x<0}(3x+1)=1=f(0)\textbf{[1]}\\\lim\limits_{x\rightarrow0,x>0}f(x)=\lim\limits_{x\rightarrow0,x>0}\displaystyle\frac{\arcsin x}{x}=1\textbf{[2]}\\\textbf{[1],[2]}\Rightarrow f\text{ continu\u a \^in }0[/tex]
[tex]\text{Studiem conntinuitatea func\c tiei f \^in }x_0=1\\\lim\limits_{x\rightarrow1,x<1}f(x)=\lim\limits_{x\rightarrow1,x<1}\displaystyle\frac{\arcsin x}{x}=\arcsin1=\frac{\pi}{2}\textbf{[3]}\\\\\lim\limits_{x\rightarrow1,x>1}f(x)=\lim\limits_{x\rightarrow1,x>1}\ln x=ln1=0=f(1)\textbf{[4]}\\\textbf{[3],[4]}\Rightarrow f\text{ nu este continu\u a \^in }1[/tex]
