Verify Roll’s Theorem for 𝑓(𝑥) = 𝑒ଶ௫2𝑥 − 𝑐𝑜𝑠2𝑥) on ቂగ଼ , ହగ଼ ቃ

If 𝑓(𝑥) = 𝑠𝑖𝑛−1𝑥, 0 < 𝑎 < 𝑏 < 1, use Mean value theorem to prove that𝑏 − 𝑎√1 − 𝑎2 < 𝑠𝑖𝑛−1𝑏 − 𝑠𝑖𝑛−1𝑎 < 𝑏 − 𝑎√1 − 𝑏2

prove 𝑓(𝑡)𝛿'(𝑡) = 𝑓(0)𝛿'(𝑡) − 𝑓'(0)𝛿(𝑡)

. 𝑓(𝑥) = 3𝑥4 − 4𝑥3

𝑓(𝑥) = 𝑥4 − 4𝑥3 + 4𝑥2

Use convolution theorem to evaluate 𝒁−𝟏[ 𝒛𝟐(𝒛−𝟑)𝟐]