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
True
False

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? ->

True
False

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.
True
False

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
True
False

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

True
False

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
True
False

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
True
False

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.
True
False

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 .

True
False

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 ? ->

True
False