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The symbols, $a$ and $T,$ represent positive quantities, and $u(t)$ is the unit step function. Which one of the following impulse responses is NOT the output of a causal linear time-invariant system?

  1. $e^{+at}u(t)$
  2. $e^{-a(t+T)}u(t)$
  3. $1+e^{-at}u(t)$
  4. $e^{-a(t-T)}u(t)$
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