Naming the Structure: The name “4-Methylpent-2-enal” provides the key structural features of the molecule. The “pent” indicates a five-carbon chain. “2-enal” indicates the presence of a double bond at the second carbon and an aldehyde group at the terminal position. The “4-methyl” substituent specifies a methyl group attached to the fourth carbon.
Construct the Structure Step-by-Step:
Step 1: Place a five-carbon chain.
Step 2: Insert a double bond between carbons 2 and 3.
Step 3: Attach an aldehyde group (C=O with an H) to the first carbon.
Step 4: Add a methyl group to the fourth carbon.
Verify Each Option: Only Option (4) matches this structure, with the correct placement of the double bond, aldehyde group, and methyl substituent.
Conclusion: The structure in Option (4) is correct for 4-Methylpent-2-enal.
Let \( y = f(x) \) be the solution of the differential equation
\[ \frac{dy}{dx} + 3y \tan^2 x + 3y = \sec^2 x \]
such that \( f(0) = \frac{e^3}{3} + 1 \), then \( f\left( \frac{\pi}{4} \right) \) is equal to:
Find the IUPAC name of the compound.
If \( \lim_{x \to 0} \left( \frac{\tan x}{x} \right)^{\frac{1}{x^2}} = p \), then \( 96 \ln p \) is: 32