设f（x）=xsin(1/x),(x>0)a+x²,(x≤0)要使f（x）在（-∞,+∞）内连续,应当怎样选择数a

Question

设f（x）=xsin(1/x),(x>0) a+x²,(x≤0) 要使f（x）在（-∞,+∞）内连续,应当怎样选择数a

Answer 1

左极限f(0-)=lim{x->0-}a+x^2=a
右极限f(0+)=lim{x->0+)xsin1/x=0
f(0)=a
要f(x)在(﹣无穷,+无穷)连续必须且仅需f(0-)=f(0+)=f(0),即a=0