Math 1431
LAB session 2
Log in your CASA account, open Attendance Lab 2
)0
Quiz 3
1
Continuity
of functions
C) 1
D)
E) 1
18
4
8
F)
1
15
Example 1: Is the following function continuous at x=2
f (x) = |x3
B) 0
C)
1
18
8|
D)
1
4
E)
1
8
3
F)
1
15
f (x)2:=Is|xthe following
8|
Example
function continuous at x = 4
8 2
x
>
if x < 4
<4
f (x) = 5
if x = 4
>
:
x + 2 if x > 4
5x
x! 2
D) 49
⇡
9
0
4⇡
D)
9
Example
3: If possible redefine f(x) to make it continuous at x=2
f (x) =
x2
5x + 6
x 2
1
Question #
C)
1
18
D)
f (x) = |x3
1
4
E)
1
8
F)
1
15
8|
8 2
x
>
if x < 4
<4
f (x) Question
= 5 # if x = 4
>
: following function continuous at x=5?
Is the
x + 2 if x > 4
p
x+3
f (x) =
x 5
A) Yes
B) No, jump discontinuity
C) No, infinite discontinuity
D) No, removable discontinuity
t
8 2
x
>
if x < 4
<4
f (x)Quiz
=45
if x = 4
Example
4:
>
:
x + 2 if x > 4
Can the intermediate-value
theorem be used to show there is a solution for
p
the equation f(x)=0
x + 3 on the interval [1,6] for the following function? Give an
f (x) = why.
explanation
x 5
f (x) = x2 + x
B) 0
C)
1
18
D)
10
1
4
f (x) = |x3
E)
1
8
F)
8|
8 2
x
>
if x < 4
<4
f (x) = 5
if x = 4
>
:
x + 2 if x > 4
p
x+3
f (x) =
x 5
f (x) = x2 + x
10
Example 5: Solve the inequality
(x + 4)(2x
6)(x
2
5)
0
1
15
Example 6a:
Is it possible to have a function f defined on [ 1 , 9 ] and meets the given conditions?
f is continuous on [ 1 , 9 ], takes on the values -5 and 2 but does not take on the value 0.
Example 6b:
Is it possible to have a function f defined on [ -1 , 3 ] and meets the given conditions?
f is continuous on [ -1 , 3 ], has a maximum value of 10 and a minimum value of 10.
Question #
Is it possible to have a function f defined on [ -2 , 3 ] and meets the given conditions?
f is continuous on [ -2 , 3 ], takes on the values 5 and 10 but does not take on the value 0.
A) No
B) Yes
Quiz 5
to write
a thesis
Daria Kurzanova
sin x
lim
=1
x!0 x
March,2015
Example 7:
sin 3x
x!0 7x
lim
to write a thesis
Daria Kurzanova
March,2015
Example 8:
sin 3x
lim
x!0 sin 4x
1
1
March,2015
Question #
sin 4x
x!0 9x
lim
A) 94
B)1
2 cos x
lim⇡
x! 2
5x
C)0
D) 49
w to write a thesis
Daria Kurzanova
March,2015
Example 9:
sin 2x2
lim
x!0 5x2
1
1
1
ow to 1write
a thesis
cos x
lim
x!0
=0
x
Daria Kurzanova
March,2015
Example 10:
cos 3x
x!0
5x
lim
1
=0
w to write a thesis
Daria Kurzanova
March,2015
Example 11:
cos x 1
lim3⇡
1 3x
x! 2
1
March,2015
Example 12:
5x
x!0 tan 2x
lim
How to write a thesis
w to write a thesis
Daria Kurzanova
Daria Kurzanova
March,2015
March,2015
Question #
lim⇡
x! 2
A) 94
2 cos x
5x
B)1
2
A)- 5⇡
B) 2⇡
5
1
lim⇡
1
x! 2
C)0
D) 49
C) 3⇡
9
D) 4⇡
9
2 cos x
5x
1