pham (ttp484) HW12 neitzke (52655)
This print-out should have 24 questions.
Multiple-choice questions may continue on
the next column or page nd all choices
before answering.
1
5
4
4
3
001
10.0 points
If g(x) is continuous on [a,b] and m is a
constant, de
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Quiz 3a 15min
1) Let x2(1 + y) = y2
a) Use implicit differentiation to solve for fitg; use %%-notation.
b) Find all pairs P(x, y) where %g = 0.
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21) Use %n0tation and implicit differentiation to solve for
Quiz 3a 15min
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calculus sin frontera
1
Section 1.x: The Variety of Asymptotic Experiences
We talked in class about the function y = 1/x when x is large.
Whether you do it with a table
x-value
y = 1/x
10
100
1000
0.1
.01
.001
or with a graph (see Figure 1), the result is
calculus sin frontera
1
Section 2.8: The Power Chain Rule
I want to see what happens when I take a function I know, like
g( x ) = 1 x2 , and raise it to a power, f ( x ) = (1 x2 ) a :
(1 x2 )2 if a=2
2 a
1
f ( x ) = (1 x ) = 1 x 2
if a=-1
1 x2 if a = 1
2
Quiz 1a 15 min
Show All Work
1
1
1' 3
mini/m
A 1;} l,
I 7 : X z:
X x032:
x'\
x
1M «9 .: 15w 1% Quiz 1b
15 min
Show All Work
limx3+2332zc2 : 44,1; 0.
awkf mg mL ><~l
l ArL
_7£.'531 1. X-z =
(X3 ._ ¥7\ X3_>< 1( 252?
, 2,1
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4 g
Q1 10am
Book
Problems
Q1 Info
Q1 10am
Practice
Q1 for 10am class: Thursday Sept 1. Covers removeable discontinuities
Q1 for 11am class: Thursday Sept 8. Covers jump, asymptote discontinuities
Use algebraic techniques to find the limits:
x3 + 2x2 x 2
d) l
Quiz 2a 20 min No Calculators Show All Work!
Let
x4+1
f($)_133+13
a) Find all vertical asymptotes
b) Find a g to which f is asymptotic.
d) Show f is asymptotic to g, by computing the appropriate limit.
2 - (51W (y: WV) "0
C.) C(w/IOIb- 0
Yr!) /
f /
L
pham (ttp484) HW13 neitzke (52655)
This print-out should have 24 questions.
Multiple-choice questions may continue on
the next column or page nd all choices
before answering.
001
keywords: IntSubst, IntSubstExam,
002
I =
/4
1. I = 2
x2
+3
2
2. I =
2. I =
Projected Grades
Using the Projected Grades sheet:
1) Your grades were sorted by q1, q2, e.1 Knowing those grades will tell you which line is yours; if
you like you can cross check with the other quizzes too.
2)If one of the grades is wrong, bring the exa
calculus sin frontera
1
More For You: Detox
Problem:
Heres a more complex word problem: MDMA is an illegal psychoactive substance with an average half-life of 8 hours in the body. Drug
tests can detect it in blood concentrations as low as 500 ng/mL.
If yo
Exam la} 50 minutes Show All Work! No Calculators
1)(30 points) Let f be dened as
a) Factor a sign/um function from f.
b) Use a) to write f as a piecewise dened function.
C) Use b) to determine if f has a jump discontinuity at 1.
X>/
"22:1 .9: x p ,
0 /
calculus sin frontera
Section 2.7: Derivative Formulae
I want to talk about some of the basic derivative formulae: product, quotient, chain rules. There are all kinds of ways to think about
these: geometrically or algebraically, using limits. Well do some
calculus sin frontera
1
Section 2.11: Hyperbolic Functions
This section is, well, its practice: with the algebra of exponentials.
You know me: the section is absolutely infested with ulterior motives
too. Enjoy!
Everyone of course immediately remembers ou
calculus sin frontera
Section 2.13: The Calculus of Force
We all have an intuitive sense of force, even from early childhood:
push a toy, it moves away; pull, it moves towards us. Children get
this very early. Mathematicians and physicists, not so much.
R
calculus sin frontera
Section 1.x: Weird Limits
Level II Alert This one goes out to all those strange limits that noone loves. Well start with limx sin( x ). A little graph shows sine
doesnt look remotely like it has a limit it wobbles between +1 and
-1 a
calculus sin frontera
Section 1.y: Why Wont We Use Calculators
Partly, the same reason you cant use LHospitals Rule for computing
limits: you youre practicing the skills you need for the rest of the
course. The other part is, calculators have some issues
calculus sin frontera
Section 1.x: Why We Wont Use LHospitals Rule
I was online with a high school AP teacher a few years ago. Call him
Mr. Sagredo. He asked, "Whats the deal with you people at UT?
Youd help our students a lot if you let em use LHospitals
Version 118 exam 3 radin (55095)
This print-out should have 11 questions.
Multiple-choice questions may continue on
the next column or page nd all choices
before answering.
001
10.0 points
If F (x) is dened by
1. I =
tan3 d
sec3 d correct
sin3 sec2 d
tan2