HW #11
Find f'ljxj. f[xj|, and fwm.
1
fixl=
"I
x; = 103'
1
f[xj| = 1103:?
What is the: value Inf x} at x = 2'?
fix}: 2
Substitute x =2, f'IIxJ = l and x) =2 into the: ganaml darivatiw, xfx} i x}.
2 ' l 1 2 Substituta.
4 Simplify.
Xf'EXJ * fixlllx
Calculus with business applications, Lehigh U, Lecture 10 notes Spring 2014
1
Derivative basics
1. As noted in the last lecture, we do not want to always do the algebra of working out
the derivative using the denition. We would be doing the same computati
Calculus with business applications, Lehigh U, Lecture 04 notes Spring 2014
1
Exponentials and logarithms
1. Exponential functions are described in the text pages 23-24. For all bases the graph
contains the point (0, 1). For dierent bases, the slope of th
Calculus with business applications, Lehigh U, Lecture 03 notes Spring 2014
1
Lines and quadratics
1. Polynomials, functions in which each term is a positive integer power of the independent variable, include familiar special cases, lines and quadratics.
Calculus with business applications, Lehigh U, Lecture 02 notes Spring 2014
1
Algebra review
1. Inverse functions are dened in the text pages 24-26. We will use this basic concept
when dening logarithms. Otherwise we will stick to the basic algebra for in
Calculus with business applications, Lehigh U, Lecture 07 notes Spring 2014
1
Limits at innity
1. A limit at innity lim f (x) or lim f (x) describes the end behavior of f (x).
x
x
That is, what happens for large x or negative x with large absolute value.
Calculus with business applications, Lehigh U, Lecture 08 notes Spring 2014
1
Continuity
1. Informally think of a continuous function as one that you can draw without lifting
your pencil. That is, it has no holes or breaks. We rst dene continuity at a poi
Calculus with business applications, Lehigh U, Lecture 05 notes Spring 2014
1
Trigonometric functions
1. Trigonometric functions often arise in physical applications with periodic motion.
They do not arise often in business examples. We will still cover t
Calculus with business applications, Lehigh U, Lecture 09 notes Spring 2014
1
Denition of derivative
1. To get the slope the tangent to f (x) we look at the slope of the secant line between
the points (x, f (x) and (x + h, f (x + h) and take the limit as
Calculus with business applications, Lehigh U, Lecture 06 notes Fall 2013
1
Limits
1. Look at Example 1, text pages 50-54. The position of a rocket in feet, launched at a
initial velocity of 96 feet per second after t seconds is given by s(t) = 16t2 + 96t
Calculus with business applications, Lehigh U, Lecture 01 notes Spring 2014
1
Functions
1. A company sells 100 widgets at a price of $20. Sales increase by 5 widgets for each
$1 decrease in price. Write an expression for the number, q, of widgets sold in
Name:
Section Number:
September 27, 2016
Math 81 Quiz 2
1.) For each of the following, either find the limit, or show that it does not exist. Show all work.
4x4 y 3 + 3x2 y + 2
x!1
x6 y 3 + 2x3 y 2
4x4 y 3 + 3x2 y + 2
y!1
x6 y 3 + 2x3 y 2
(a) lim
(b) lim
Name:
Section Number:
September 29, 2016
Math 81 Quiz 2
1.) For each of the following, either find the limit, or show that it does not exist. Assume x and y are
positive. Show all work.
3x3 y 2 + 4xy 5 + 2x
x!1
x2 y 5 + 2xy 2
3x3 y 2 + 4xy 5 + 2x
y!1
x2 y
Lehigh University.
Calculus with Business Applications - Math 81 Quiz 1 Version B
September 16 2016
% l D
Name b bl lo Recitation Section Number
Instruction: This is a closed book quiz. Put all cell phones and electronic devices away; they are not to be
u
LEHIGH U MATH 81 —' CALCULUS WITH BUSINESS
APPLICATIONS
FINAL EXANI DEC 19, 2011
December 19, 2011 Name 7)
Section
Grading
1 11.
2. r 12.
3 13.
4 .14.
5. 15.
6 16.
7 17.
8 18.
9 19.
10. 20. w
Total
This is a closed boot: exam. No books, notes or other aid
HW #4
25
Th 1" , E}=.
EIEDI'E: use 24
(2110055: the currth irzlvantityrr fur cut E}.
1
use [i
1
52: E}
until:
until:
Th-1
24
Substitut: ? fur tan {1 intn the idtit}? and simplify.
1
WW:
ta
11E]
1
24
T
_ T
"E
[Type an integar ur a simplied fractinn.)
T
Hw #9
Evaluate the limit of the compusition by direct substitutictn.
36-
1' 54 53 135:5134 so 1
xtx x J {(3 (it)
Simplify.
- 4 a an 35
titling" 5" =(snnt 50303 1]
"I
= 1
Therefore, limIZSJt:4 5x3 HE'S: .
xH]
Suppose 86500 is invested in a savings account
HW #8
The common factor is 311: + 231.
Now cancel out the common factors and write it} into reduced form.
Note that if x) is in reduced form, then the vertical asymptotes occur at the zeros of the
denominator.
Select the correct choice below and, if nec
HW #2
T
Th 1" , E]=.
ere ore cos 25
Determine the value of sin El using the trigonometric ldntllji sinz t on 52E} = l.
sinEE] t eosz = l
sinz = l eosz Subtract eosg from both sides.
sin E] = i- 1 cos 2E} Use the square root property.
7 2 . T
- _ s htt t r
Hw #5
' 42 Simplify.
[Type an integer er decimal reunded te three decimal places as needed.)
The completed table shewing the average yele eity fer each time interval is shown below.
Time Interval [l 2] [19,2] [1.99, 2] [l.999,2] [19999.2]
53 42.16 42.916
HW #6
B}; the difference limit 111W1 lim[fl:x} gxj] = limflx] limgx].
xi xht xHt
it
Use ie difference limit law.
111111711111 S'tj=lTEIliml:1 s";
tI'DC tI'DC
=1re[1im 1 lim 5*]
tI'DC ti'DC
Find the limits.
11111171111 5_tj=lTD[liml lim5_t]
tI DC I? DE: ti
HW #1
Find thc Exact value 111" Each iii" the ramaining trigonometric funciinns [If E].
3
ans 3 = E, in quadrant II
If P = {my} is El point [in 1:1]: unit circla canaspnnding to U, than 111': fullnwing Ell": tma.
F
51:13:}? 43053:}: tanEJ=,ifxi
x
l _ 1 _