In "The Second Coming" by W. B. Yeats, the speaker asserts that the best people "lack all conviction, while the worst / Are full of passionate intensity." How does this statement apply to the speakers in "An Irish Airman Foresees His Death" by Yeats and "The Love Song of J. Alfred Prufrock" by T. S. Eliot? What characteristics of the modern world make it difficult, if not impossible, to be heroic in the traditional sense?

When answering this question, keep in mind the context of the poem in question: "The Second Coming" was written in 1919, amid a time of deep disillusionment in Europe. So, when thinking about the meaning of the lines in question, I'd suggest you think of it in terms of the very real soul-searching that characterized this period in history. How might you expect individuals to view their political leaders, as well as the future, especially given the experience of the First World War? What kind of vision does "The Second Coming" present, as far as it relates to those same kinds of questions? I think the lines in question are a very powerful illustration of the sense of disillusionment and cynicism that awakened in the time period in question.
From here, it's a matter of applying this same kind of thinking to the other two poems. When looking at "An Irish Airman Foresees His Death," it's worth asking: just what is the man's attitude toward the war as far as it relates to the enemy? to his own side? to himself? Similarly, consider the psychology of Prufrock. How does Eliot depict the world, as well as the character of Prufrock? Do we see the same modernist impulses at play? In thinking about these poems in these terms, I think you should be able to discern how they fit together in the manner your question asks for.