Math 1431
Section 14819
TTh 10-11:30am 100 SEC
Bekki George
bekki@math.uh.edu
639 PGH
Office Hours:
11:30am – 12:30pm TTh and by appointment
Class webpage:
http://www.math.uh.edu/~bekki/Math1431.html
Test 2 is 10/1-10/3!
Save your confirmation email. Note that if you miss your time or
are late, you will lose your seat and may get a 0 on the test.
Your final exam does replace your lowest test grade.
Test 2 covers sec 1.2-3.2
Practice Test 2 counts as bonus (5% added to test 2).
Review sheet will be turned in as your lab quiz grade on Oct 1.
EMAIL ME QUESTIONS FROM THE REVIEW SHEET BEFORE
5:00 PM ON MONDAY AND I WILL INCLUDE THEM IN THE
NOTES!
Some review problems:
lim
x 3
lim
x®8
lim
x®-2
x 3
2
x  2x  3
( x - 8 ) ( x - 3) =
2
x -9
( x - 8 ) ( x - 2) =
2
x -4
lim
x 3
x3  6
x 3
5x
lim
x  0 sin 2x
sin x
lim
=
x®0 4x
sin 3x
lim
=
x®0 sin 4x
lim
x®0
1 - cos x
=
x
 x2  1 x  1
f x  
x 1
4
Which are true?
A) lim f ( x ) exists
x®1
B) f (1) exists
C) f is continuous at x = 1
 x2  x

f x   x
1
x0
x0
Which are true?
A) lim f ( x ) exists
x®0
B) f (0) exists
C) f is continuous at x = 0
ì
3x ( x - 1)
for x ¹ 1, 2
ï f (x) =
( x - 1) ( x - 2 )
ï
ï
Suppose í f (1) = -3
ï
ï f (2) = 4
ï
î
Then f (x) is continuous
A) except at x = 1
B) except at x = 2
C) except at x = 1 or 2
D) except at x = 0, 1, 2
E) at each real number
Derivatives:
y  17x  24x
1
2
g    sin  sec  
 
w  x   tan x
2
 
f  w   cot w  cot w
2
2
f (x) =
2
x + 5x + 2
x + 1
æ x + 2x ö
f (x) = ç
÷
x
è
ø
3
5
g    sin
2
 2      2
g  x   cos  2  3x 
Use implicit differentiation to find y' if x 3 + 4y2 = 17 .
Find the equation of the tangent line for above equation at the point
(1,-2)
Where is f ( x ) = 2 - x not differentiable?
Suppose f ( x ) =
x=2? At x=-2?
x-2
2
x -4
. Is it possible to define f to be continuous at
Use the definition of the derivative to find the derivative of
1
f x 
x 3
f x  x  2
Let
Find
f ( 3) = 1, f ' ( 3) = 2,
h' ( 3) if h ( x ) = f ( x ) g ( x ).
g ( 3) = 4,
g' ( 3) = 6 .
More related rate problems:
1. Maple and Main Streets are straight and perpendicular to each
other. A stationary police car is located on Main Street ¼ mile from
the intersection of the two streets. A sports car on Maple Street
approaches the intersection at the rate of 40 mph. How fast is the
distance between the two cars decreasing when the sports car is 1/8
mile from the intersection?
2. Water is pouring into an inverted cone shaped tank at the rate of
20 ft3/min. The tank is 10 ft. tall and has a radius of 4 ft. How fast
is the height of the water rising when it is 5 ft deep?
3. A small boat is 90 feet offshore, and moving parallel to a straight
beach. The boat is moving at a constant speed of 10 feet per second.
At time t = 0 the boat is directly opposite a lifeguard station which is
40 feet from the water. How fast is the boat moving away from the
lifeguard station when the distance between the boat and the lifeguard
station is 150 feet?
4. A pile of trash in the shape of a cube is being compacted into a
smaller cube. Suppose the shape is always a cube and the volume is
decreasing at the rate of 3 cubic meters per minute. Find the rate of
change of an edge of the cube at the instant that the volume is exactly
64 cubic meters.
5. A point moves around the circle x2 + y2 = 9. When the point is at
- 3 , 6 , its x coordinate is increasing at the rate of 20 units per
(
)
second. How fast is the y coordinate changing at that instant?
6. A screen saver displays the outline of a 3 cm by 2 cm rectangle
and then expands the rectangle in such a way that the 2 cm side is
expanding at the rate of 4 cm/sec and the proportions of the rectangle
never change. How fast is the area of the rectangle increasing when
its dimensions are 12 cm by 8 cm?
POPPER 07
1.
Find
dy
if x + cos ( x + y ) = 0.
dx
A) csc x + y - 1
(
)
B) csc ( x + y )
C)
D)
E)
x
sin ( x + y )
1
1- x
2
1 - sin x
sin y
2.
Find
A)
dy
3
dx
2
3x
x - 3y
2
2
B)
C)
3x - 1
1 - 3y
E)
2
2
3y - x
2
D)
2
y - 3x
2
3x + 3y - y
x
2
2
3x  3y
x
3
if x - xy + y = 1.
3. Find h ¢ ( x ) if h  x   f  g  m  5x   
( )
( (
( )))
( )
((
( )))
( )
((
( ))) g ¢ ( m¢ (5x ))
( )
((
( ))) g ¢ ( m (5x )) m¢ (5x )
A) h ¢ x = 5 f ¢ g ¢ m¢ 5x
B) h ¢ x = 5 f ¢ g m 5x
C) h ¢ x = 5 f ¢ g m 5x
D) h ¢ x = 5 f ¢ g m 5x
E) none of these
#4-6 are all B