12.4. Properties of Dirac Delta Function

Try these first

1. 1.

   What is the property of the Dirac delta function concerning symmetry?

   Hint

   Think about how the function behaves on both sides of the origin.

2. 2.

   How do you express δ(ax) in terms of δ(x)?

   Hint

   Consider how the function scales.

3. 3.

   What is the value of δ(0)?

   • 1
   • 0
   • ∞

   Hint

   Remember how the function behaves at its central point.

4. 4.

   The property δ(-x) = δ(x) defines what characteristic of the Dirac delta function?

   • True
   • False

   Hint

   Think about symmetry.

5. 5.

   A force F is applied at x=5 and modeled as Fδ(x-5). How would you express the total force over the region from x=0 to x=10?

   Hint

   Focus on the bounds of the integral and where δ(x-5) has an impact.

6. 6.

   Consider a shifted delta function δ(x-2) in an integral from 0 to 5. What would the integral yield?

   Hint

   Identify the limits and the point where δ(x-2) is non-zero.