In each of 1 through 6, determine whether the method of separation of variables can be used to replace the given partial differential equation by a pair of ordinary differential equations. If so, find the equations.xuxx + ut = 0

Lecture 27 L’Hˆopital’s Rule (Section 4.5) Consider the following limits: e − 1 ex. lim x→0 x ln(x) ex. x→∞mx +1 These limits are Indeterminate Forms and ∞ .e 0 ∞ have seen how to evaluate some limits of this form, but the process can be complicated. √ 2 ex. lim x +3 − 2 x→1 x − 1 sinx lim x→0 x