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The Dirac delta function $\delta(t)$ is defined as

1. $\delta(t)= \begin{cases}1, & t=0 \\ 0, & \text { otherwise }\end{cases}$
2. $\delta(t)= \begin{cases}\infty, & t=0 \\ 0, & \text { otherwise }\end{cases}$
3. $\delta(t)=\left\{\begin{array}{ll}1, & t=0 \\ 0, & \text { otherwise }\end{array}\right.$ and $\int_{-\infty}^\infty \delta(t) d t=1$
4. $\delta(t)= \begin{cases}\infty, & t=0 \\ 0, & \text { otherwise and } \int_{-\infty}^{\infty} \delta(t) d t=1\end{cases}$