In 31 and 32 discuss whether product solutions u X(x)Y(x) can be found for the given partial differential equation. [Hint: Use the superposition principle.]2ux2 u 0

L7 - 4 Inﬁnite Limits Def. Let f be deﬁned on both sides of c,e ctpsly at c.x→c f(x)= ∞ if the values of f(x)c anbemaeand kept) as large as we want by taking x suﬃciently close to c but not equal to c. x=c x=c Also, lim f(x)= −∞ means the values f(x) < 0c nbe x→c made (and kept) as large as possible in absolute value as we want by takingx suﬃciently close but not equal to c. NOTE: Similar deﬁnitions can be given for approaching c from the left or right. Def. The line x = c is called a of the curve y = f(x)iftatonefheowngsre: