AP Calculus AB – Chapter 1 Test
NAME_____________________________
1.
Decide if each problem requires Calculus? If not, solve.
a) Find the length of the graph f(x) = 2x-3 from the point
(1,1) to the point (4,5) _________________
b) Find the length of the graph g(x) = x2 – 3 from the point
(1,-2) to the point (3,6) ________________
2. Describe three different reasons that a limit might fail to exist. You may draw a diagram
to illustrate each situation, or simply describe it.
3. Use the NUMERICAL method to determine the following limit:
Set up a table of values and include 3 values on either side of -5.
x
f(x)
4. Define f(x) =
a) Show that f(x) is continuous at x = 5.
b) Where on the interval [1,4] is f NOT continuous? Show/explain how you know.
.
5. Use the graph at the right to answer questions a) through d).
6
a)
b)
c)
lim f(x) =
x →2
lim
f(x) =
lim
f(x) =
x →4 
x → 4- -
f
4
2
-10
-5
5
10
-2
d)
lim
x →0
f(x) =
-4
6. Find a c such that f(x) is continuous on the entire real line.
x 2 when x  4

f(x) =  c when
x 4
 x
7. Find the x-values (if any) at which f is discontinuous. Label as removable or nonremovable.
f(x) =
2x  6
2x 2  18
8. True or False: If f is undefined at x = c, then the limit of f(x) as x approaches c does not
exist. If false, provide a counterexample, such as a graph.
9. Verify that the Intermediate Value Theorem applies to f(x) = x2 + x – 1 on the interval
[0,5], f(c) = 11. Find the value of c.
10. Find the vertical asymptotes of the graph of