24F(x)=0"* +1' **0, then 1 0 , x=0 (a) lim f(x)=0 (c)f(x) is discontinuous at x=0 (b) lim f(x)=1 (d)f(x) is continuous at x=0 x0

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( f(x)=left{begin{array}{cc}frac{1}{1 / x+1} & , x eq 0 0 & x=0end{array}right. ) (a) ( lim _{x rightarrow 0^{-}}left(frac{1}{x}right)=-infty ) ( lim _{x rightarrow 0^{-}} e^{y x}=0 Rightarrow lim _{x rightarrow 0^{-}} frac{1}{e^{y_{x+1}}}=frac{1}{1} ) ( (b) mid lim _{x rightarrow 0^{+}}left(frac{1}{x}right)=infty ) ( S ) ( lim _{x rightarrow 0^{+}} e^{y x}=infty Rightarrow lim _{x rightarrow 0^{+}} frac{1}{e^{x} x+1}=0 ) ( fleft(lim _{x rightarrow 0^{+}} f(x) eq lim _{x rightarrow 0^{-}} f(x) eq f(0)right. ) So dis continuour ( f(7) ) is dis continuas

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