(a) Find the coordinate vectors and of x with respect to the bases B and C, respectively. (b) Find the change-of-basis matrix from B to C. (c) Use your answer to part (b) to compute and compare your answer with the one found in part (a). (d) Find the change-of-basis matrix from C to B. (e) Use your answers to parts (c) and (d) to compute and compare your answer with the one found in part (a).

L27 - 2 We introduce a new method that applies to many limits of this form: L’Hˆ opital’s Rule ▯ Suppose that f and g are diﬀerentiable and g (x) ▯=0er a (except possibly at a). Suppose that lim f(x)=0a ndl g(x)=0 x→a x→a or x→a f(x)= ±∞ and lim x→a)= ±∞. Then if it exists or is ±∞ . Note the following: 1. L’Hˆpital’s rule applies to one-sided limits and limits at inﬁnity. 2. L’Hoˆpital’s rule is the limit of quotient of derivatives, not the limit of derivative of the quotient.