Assignment 2 and 3

Math 460

Quiz 2

1) Represent 𝒇(𝒙) = 𝐬𝐢𝐧 𝒙 𝒊𝒇 𝟎 < 𝒙 < 𝝅 and 0 if 𝒙 > 𝝅 as the Fourier Cosine

Integral.

2) Represent 𝒇(𝒙) = 𝐜𝐨𝐬 𝒙 𝒊𝒇 𝟎 < 𝒙 < 𝝅 and 0 if 𝒙 > 𝝅 as the Fourier Sine

Integral.

3) Find the Fourier Sine transform of 𝒇(𝒙) = 𝒙𝟐 𝒊𝒇 𝟎 < 𝒙 < 𝟏 and 0 if 𝒙 > 𝟏.

4) Find the Fourier transform of

𝒇(𝒙) = 𝒆−|𝒙|

for −∞ < 𝒙 < ∞.