Question

1-11 Simplify the following expressions: (a) \left(\frac{\sin t}{t^2 + 2}\right)\delta(t) (c) \left[e^{-t}\cos \left(3t - 60^\circ\right)\right]\delta(t) Hint: Use Eq. (1.23). For part (f) use L'Hôpital's rule. 1-12 Evaluate the following integrals: (e) \int_{-\infty}^{\infty}\delta(t + 3)e^{-t}dt (f) \int_{-\infty}^{\infty}(t^3 + 4)\delta(1 - t)dt

          1-11 Simplify the following expressions:
(a) \left(\frac{\sin t}{t^2 + 2}\right)\delta(t)
(c) \left[e^{-t}\cos \left(3t - 60^\circ\right)\right]\delta(t)
Hint: Use Eq. (1.23). For part (f) use L'Hôpital's rule.
1-12 Evaluate the following integrals:
(e) \int_{-\infty}^{\infty}\delta(t + 3)e^{-t}dt
(f) \int_{-\infty}^{\infty}(t^3 + 4)\delta(1 - t)dt

1-11 Simplify the following expressions:
(a) ((sint)/(t^2 + 2))δ(t)
(c) [e^-tcos(3t - 60^∘)]δ(t)
Hint: Use Eq. (1.23). For part (f) use L'Hôpital's rule.
1-12 Evaluate the following integrals:
(e) ∫-∞^∞δ(t + 3)e^-tdt
(f) ∫-∞^∞(t^3 + 4)δ(1 - t)dt

Added by Juan T.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Kirsty Gledhill

Step 1

So, sin(t^2) simplifies to (1/2)[cos(2t^2) - 1]. Show more…

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1-11 Simplify the following expressions: (a) sin(t^2) (c) [e-cos(3t)-60]t Hint: Use Eq. 1.23. For part (f), use L'Hopital's rule. Evaluate the following integrals: (e) 8t+3e^(-t) (f) t+481-t^2 dt