1. Let $1 = 1 and Sn+1 = (" )s, for n > 1. (a) Find $2, $3 and $4. (b) Show lim s, exists. (c) Prove lim s, = 0. 2. Let $1 = 1 and Sat1 = (Sn + 1) for n 2 1. (a) Find $2, s3 and $4. (b) Use induction to show s. > , for all n. (c) Show (s,) is a decreasing sequence. (d) Show lim s, exists and find lim s. 3. Accept on faith that the following familiar functions are continuous on their domains: sin x, cos x ex,2%, log, x, for x > 0, xP for x > 0 and p any real number. Use these facts and the theorems on continuity to show that the following functions are also continuous Note: family names starting with the letter in A - L will answer (a) and ( c) family names starting with the letter in L - Z will answer (b) and ( d) ) (a) loge(1 + cos* x) (b) [sin x + cos x]" (c) 2x2 (d) 8x