Question

sa se determine numarul real a astfel incat functia f sa fie continuia in x=1​

Answer 1

$\text{f continu\u a \^in }x_0=1\Leftrightarrow \lim\limits_{x\rightarrow1,x<1}f(x)=f(1)=\lim\limits_{x\rightarrow1,x>1}f(x)\\\\\displaystyle\lim\limits_{n\rightarrow1,x<1}f(x)=\lim\limits_{n\rightarrow1,x<1}\frac{x^2+3}{x^2+1}=\frac42=2=f(1)\\\\\displaystyle\lim\limits_{n\rightarrow1,x>1}f(x)=\lim\limits_{n\rightarrow1,x>1}\frac{ax+2}{x^2+1}=\frac{a+2}{2}\\\\\\\displaystyle\frac{a+2}{2}=2\Rightarrow a=2$