3. Assume that f is uniformly continuous on a bounded set S, prove that f(S) is bounded. (hint: thm 19.4, 11.5) 4. Let ƒ(x) = (x-1)(x−3)² , ‚ determine limä→1 ƒ (x), limx→2 ƒ (x), limx→3 ƒ (x). (hint: limit may be infinite or does not exist).

7. Show that the limit does not exist by approaching (0,0) along different paths. lim + y- (x, y)→(0,0)

2. Evaluate the limits numerically. x-1 a) lim x→1 vx+3-2 x² +3x+2 b) lim x→-1 x²-x-2 cos(x)-1 c) lim x2 ズ→0

3. Consider the function f(x) : (0, ∞) → R where f(x) = =. (1) Show by definition that f is continuous at every > 0. (2) Show that f does not have a right limit at 0.