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Let f: R be a function. We say that f has PROPERTY 2 if lim_(hto0)(f(h)-f(0))/(h^2) exists and is finite. Then which of the following options is/are correct ? |
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Answer» `f(x)=sinx` has PROPERTY 2 property 2, `underset(hto0)(lim)(f(h)-(f(0)))/(h^(2))` exists and finite. OPTION a, `P2:underset(hto0)(lim)(h^(2//3)-0)/(sqrt(|h|))=underset(hto0)(lim)(1)/(h)((sinh)/(h))=`doesn't exist. option b, `P1:underset(hto0)(lim)(|h|-0)/(sqrt(|h|))=underset(hto0)(lim)(|h|)/(h)={{:(1,"if "hto0^(+)),(-1," if "hto0^(-)):}` so `underset(hto0)(lim)(f(h)-f(0))/(h^(2))` does not exist. |
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