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Math 1431
Section 12485 MWF 12‐1pm SR 117
Dr. Melahat Almus
almus@math.uh.edu
http://www.math.uh.edu/~almus
COURSE WEBSITE:
http://www.math.uh.edu/~almus/1431_sp16.html
Visit my website regularly for announcements and course material!
If you e-mail me, please mention your course (1431) in the subject line.
Check your CASA account for quiz due dates; don’t miss any quizzes.
BUBBLE IN PS ID VERY CAREFULLY! If you make a bubbling mistake, your scantron will not be saved in the system and you will not get credit for it even if you turned it in.
Bubble in Popper Number.
DID YOU RESERVE A SEAT FOR TEST 2? REVIEW FOR TEST 2 is posted on course website! Test 2 covers Chapters 1 and 2, and Section 3.1.
Be considerate of others in class. Respect your friends and do not distract anyone during the lecture.
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Popper #
x(t) = -16 t2 +320 t .
Question# How long does it take to reach the maximum height?
a) 10 seconds b) 5 seconds c) 15 seconds d) 20 seconds e) None
Question# What is the maximum height?
a) 1600 b) 3200 c) 3040 d) 2400 e) None
Question# How long does it take to hit the ground?
a) 10 seconds b) 20 seconds c) 16 seconds d) 32 seconds e) None
Question# What is the speed on impact?
a) -320 ft/sec b) 320 ft/sec c) 160 ft/sec d) -160ft/sec e) None
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Review for Test 2
Material covered: Chapter1, Chapter 2, Section 3.1.
Number of questions: ??
?? multiple choice questions (Total: ?? points)
?? free response questions (Total: ?? points)
The multiple choice part will be graded automatically. The grade you see after your test is for the MC part only – out of ?? points. FR part will be graded later.
Time: 50 minutes
Time is limited on the test- to be able to finish the test, make sure you practice a lot and you can solve questions quickly. Knowing the material is not enough – you need to solve the problems quickly.
Take practice test 2; 5% of your best score will be added to your test grade.
Reserve a seat for Test 2. Double check your time!
Don’t be late to your test! If you’re more than 10 minutes late, CASA will not let you in.
Bring Cougar ID to the test.
No calculators.
How to study:
Solve the problems on the review sheet.
Take practice test (several times if needed).
Rework old quizzes and Hw problems.
Go over class notes.
Must know the unit circle!
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Review Problems
1. Evaluate the following limits if they do exist.
2
31
2
4 1x
x xlim
x x
2
31
2
x
x xlim
x x
2
32
3 2
4x
x xlim
x x
16
4
16x
xlim
x
5
02
12
15x
xxlim
x
2. Evaluate the following limits if they do exist.
0
5
2x
sin xlim
sin x
2
20
6
7x
sin xlim
x
0
4
9x
tan xlim
tan x
0
1 2
6x
cos xlim
sin x
6
2
20
4
5x
xlim
tan x
3.
3
2
2 1
5 1 4
4
x , x
f x x, x
x x, x
4x
lim f x ?
4x
lim f x ?
4x
lim f x ?
1x
lim f x ?
1x
lim f x ?
1x
lim f x ?
Note: Must know how to answer similar questions given a graph.
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4. Find the points of discontinuity (if any). Classify each as removable, jump or infinite.
3
2
1
2 1 2
2
x x, x
f x , xx
x x, x
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5. Find A and B so that f (x) is continuous:
2
2
1 1
( ) 4 1
3 1
x x
f x Ax x
Bx x
6. Find A and B so that f (x) is differentiable everywhere:
2 1 1
( ) 2 1
Ax x
f x Bx x
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7. Find the derivative of the following functions using the definition.
a) 2 5f x x x
10
b) 5f x x
11
c) 2
4f x
x
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8. Find the derivatives of the following functions.
32
15f x x x
x
3f x x x
2 1f x x x
2
5 2
xf x
x
53 4 1f x x x
13
22f x x x
3 4f x cos x
4 2f x sin x cos x sec x
4 33 2f x tan x sec x
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9.
a) 4f x sin x cos x x ;
5
6f ' ?
b) 2 2f x x cos x ; 2f ' ?
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10. Find the equation of the tangent and normal lines to the curve:
2 3 5 4 9x y xy y at (2,1).
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11. Suppose we are given the data in the table about the functions f and g and their derivatives. Find the following values.
2
) '(2) ( ) ( ( ))
) '(2) ( ) ( ( ))
( )) '(2) ( )
( )
) '(2) ( ) ( ) ( )
a h if h x g f x
b h if h x f g x
g xc h if h x
f x
d h if h x f x g x
x 1 2 3 4
f(x) 3 2 1 4
f’(x) 1 4 2 3
g(x) 2 1 4 3
g’(x) 4 2 3 1
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Related Rates
Work all the problems in your homework and quizzes and lecture notes.
Must know basic area and volume formulas from geometry. Area: Circle, Square, Triangle, Rectangle Surface area: Cube, Rectangular Prism Volume: Cube, Cone, Cylinder, Sphere, Rectangular Prism
12. The length of a rectangle is increasing at a rate of 5 in/min and the width is decreasing at a rate of 1 in/sec. At what rate is the area changing when the width is 5 inches and the length is twice the width?
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13. Water is poured into a conical tank at the rate of 64 cubic feet per minute. If
the tank is 10 feet tall and the top of the tank has a radius of 6 feet, how fast does the radius of the water surface change when the water is 2 feet deep?
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14. Two cars are moving towards the same point. The first car started from a
point that is 100 miles away and it travels south at a rate of 40 mi/h. The second one started from a point 105 miles away and it travels east at a rate of 60 mi/h. At what rate is the distance between the cars changing one hour later?
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15. The altitude of a triangle is increasing at a rate of 5 in/min while the base is decreasing at a rate of 1 in/min. At what rate is the area of the triangle changing when the altitude is 10 in and the base is 6 in?
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16. A particle moves on the number line with position function:
3 26 1s t t t .
a) What is the velocity of the object at time t=2?
b) What is the acceleration of the object at time t=2?
c) When is this object speeding up?
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