1. 
 Identify the picture(s) in which we can see what f is doing for all values of x in the window.
I. y = 5x ^{3}– 6x^{2} with 0.4 ≤ x ≤ 0.4 II. y = 5x^{3}– 6x^{2} with 0.6 ≤ x ≤ 0.6 > Both I and II

2. 
Four different graphs of the function f(x) = 2x^{2} + 1 are shown below. Which picture best illustrates the fact that if x is within 0.06 of 2, then f(x) is within 0.5 of f(2) = 9? >

3. 
Which statement is true for the function f shown below? > If x is within 0.5 of 3 then f(x) is within 0.5 of 1.

4. 
We have a function f. We want f(x) to be within 0.5 of f(0). For which of the following functions do we have a guarantee that we can restrict x to find what we want? (x must be allowed to move the same distance from 0 in either direction, and x may not just be set equal to 0.) > II and III

5. 
If f(x) = 4 – 2x then when x – 1 < 0.5 we have a guarantee that f(x) – 2 < 1. Identify c, ε, and δ as commonly used in the definition of continuity. > c = 1, ε = 1, δ = 0.5

6. 
Let f(x) = 3x + 1. Then f is continuous at 1 with f(1) = 4. Find the largest value of δ for which if x is within δ of 1, then f(x) is within 0.5 of 4. > 0.16

7. 
Let Then f is continuous at 4 with f(4) = 2. Find the largest value of δ for which if x is within δ of 4, then f(x) is within 0.25 of f(4). > 0.5

8. 
In the formal definition of continuity at x = c, > ε describes how close we want f(x) and f(c), while δ describes how close x and c need to be.

9. 
If the function f is continuous at c, then > for every ε > 0 we can find a δ > 0 such that if x – c < δ then f(x) – f(c) < ε.

10. 
 Let , c = 0, and ε = 0.1.
Which is the largest value of δ such that if x – c < δ, then f(x) – f(c) < ε ? >
