Question: Sea f ( x ) : = x 2 s e n ( 1 x ) para f ( 0 ) : = 0 g

Sea f(x):=x2sen(1x) para f(0):=0g(x):=x2xin[0,1]fg0,1g(x)>0x0limx0f(x)=0=limx0g(x)limx0fxg(x)0yf(0):=0,y sea g(x):=x2 para xin[0,1]. Entonces tanto f como g son derivables en0,1yg(x)>0 para x0. Demostrar que limx0f(x)=0=limx0g(x)y que limx0fxg(x)no existe.
Sea f ( x ) : = x 2 s e n ( 1 x ) para f ( 0 ) :

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