Word Count : 111

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Let (S={e^{-x},, x e^{-x}}) and let (W=[S]). Define (T:W\to W) by [ T(f)=\frac{d^{2}}{dx^{2}}(f)+2\frac{d}{dx}(f). ] First compute (T) on the basis elements. For (f_1(x)=e^{-x}), [ f_1'(x)=-e^{-x}, \qquad f_1''(x)=e^{-x}. ________ _________ ___ ___ __________ ______.
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