BC 1
Non-Quiz
Name:
No Calculators!
(1)
Find each limit. No justification necessary.
lim - [x] =
x 2
lim-
x3
(2)
x +3
=
x- 3
lim+
x3
x +3
=
x- 3
Determine whether or not ƒ is continuous at x = 1. Justify using the definition of
continuity.
5x  2, x  1
f ( x)  2
x  1, x  1

(3)
3x 3 - 5x 2 + 2
=
x 
1- 4x 3
lim
Find each limit. Justify clearly.
2x 2 + 4x - 6
lim
x 3
x 2 + 3x
lim
x 
2x 3 - 6x + 2
1- 4x 3
1.
Find each limit. No work required. (2 pts each)
a.
lim
 0
d.
2
x 5
x4
lim
x4

lim
x2

x2
x2
c.
sin 2 3
2
3x  1, x  2
lim (x) if (x) = 
x2
 x  3, x  2
 ax 5

Let g  x    a  x
 2
2
 x  a
a.
b.
e.
lim
3
2 
x  1
x  1
x  1
For what values of a, if any, will lim g  x  exist? Justify your answer.
x1
(4 pts)
b.
3.
For what values of a, if any, will g(x) be continuous at x = –1. Justify
your answer using the definition of continuity. (4 pts)
Find each limit algebraically. Clearly show how you arrived at your
answers. An answer without any algebraic justification will receive little or
no credit. (3 pts each)
a.
b.
c.
lim
y 3
lim
y2  9
y3  5 y 2  6 y
z2  9
z3  5z 2  6 z
x 2 3
lim
x7
x 7
z 
.
Indicate whether each statement about function h(x) shown below is True or
False. (1 pt each)
a.
y
b.
c.
1
d.
1
e.
x
3.
lim h  x   5
x 2 
lim h  x   1
x 4
lim h  x   2
x4
lim h  x  exists.
x 2
lim h  x  exists
x3
f.
h  3 exists.
g.
lim h  x  
x3
Sketch the graph of a function (x) with all of the following features.
Assume the domain of function  is all real numbers. (6 pts)






(2) = 5
 has a removable discontinuity at x = 2.
 has a non-removable discontinuity at x = –3.
lim   x   1
x3
lim   x   1
x
lim   x   
x
3
2