MATH137 : assign4.pdf

• School: University of Waterloo
• Department: Mathematics
• Course: MATH137
• Professor: John- Paul Pretti

Document Summary

(a) lim x 2 (b) lim x 0 (c) lim x 2. |x 2| x 2 x2 sin (cid:18) 2 (cid:19) x. 2 + x x2 + 3x 1. 3x2 2x x (d) lim x x (ln(x + 1) ln(x2 1)) (e) lim (f) x2 + 2. 3x 6 lim x x6 + 5 x3) x ( (g) lim. 5x if x < 0 if 0 x 2 if 2 < x 5 if x > 5: let f (x) = Due fri, oct 11th: find the limit, if it exists. If the limit does not exist, explain why. Show that there exists x [0, 1] such that f (x) = f (x + 1). [hint: consider g(x) = f (x + 1) f (x)] lim x . 1 xn = 0: (a) suppose that f (x) is continuous at x = 0.