Analysis Homework #2
due Thursday, Nov. 4
1. Show that the set A = {x +
1
x
: x > 0} is such that inf A = min A = 2.
2. Show that the set B = {x ∈ R : |2x − 3| < 1} has no maximum.
3. Let f be the function defined by the formula
f (x) =
x3 − 8x − 3
x−3
for all x ̸= 3. Determine the minimum value attained by f .
4. Use the ε-δ definition of limits to show that lim (4x − 3) = 5.
x→2
• You are going to work on these problems Friday in class.
• When writing up solutions, write legibly and coherently. Use words, not just symbols.
• Write your name and then MATHS/TP/TSM on the first page of your homework.
• Your solutions may use any of the results stated in class (but nothing else).
• NO LATE HOMEWORK WILL BE ACCEPTED.