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{\Large {\bf 
\begin{center}
Homework 
for the first week
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I. Keener Section 4.1

No. 1.b, 5, 6, 8, 9

II. Compute 

\begin{equation}
\int_{-\infty}^{\infty}{ e^{|x|} \delta(\sin x)}\, d\, x
\end{equation}

III Let $f(x)$ be a differentiable function in $R_1$, and  let . Prove the equality of the distributions
\begin{equation}
f( \delta(x)) = f(0) + f'(\infty) \delta(x)
\end{equation}
where 
\begin{equation}
 f'(\infty)=\lim_{x\rightarrow \infty}{f'(x)} 
\end{equation}

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