1. (4 points, 2 points each) Give an example of a function that satisfies the condition given.
a. lim f(x) ≠ f(3) (x→3)
b. lim f(x) > f(1) (x→1)
2. (5 points) State whether the following statement is true or false. If it is true, then explain why. If it is false, then provide a counterexample.
‐It is impossible for a function f(x) to be continuous at x = 5 if lim f(x) (x→5) does not exist."
3. (15 points, 5 points each) Evaluate the following limits if they exist, or specify whether it equals ∞, or simply does not exist (in which case write DNE).
a. lim (x-5x+6) / (x-7x+12) (x→3)
b. lim (x-36) / (∑x-6) (x→36)
c. lim h(x); where h(x) = {4x^2 + 2x^3 - 5x + 13, x ≠ 0; sin(x), x = 0} (x→0)
4. (8 points, 2 points each) Consider the following function defined below and use it to answer parts (a) – (d).
p(t) = {sin(t), -∞ < t < 0; 3t, 0 ≤ t < 7; 3t^2, 7 < t < ∞}
a) lim p(t) (t→2)
b) lim p(t) (t→0-)
c) lim p(t) (t→5+)
d) lim p(t) (t→7)
