September 19th Lecture
1.5 Inverse Functions
Example: Convert 32 degrees C to fahrenheit or 60 degrees F to celsius
formula F= 9/5C + 32
There is a 1 to 1 (1-1) correspondence between celsius and fahrenheit
Example: Consider f(x) = x2
f is not one t
Mealky
MATH 114 FIRST MIDTERM EXAM
Lecture 1 (afternoon)
October 9, 2013
Your name:
Circle your TAs name:
Bae Jun Park, Fan Zheng, Lalit Jain, Robin Prakash, Ethan Frost
- Circle your answers.
0 Be sure to show your work and explain what you did. You will
September 24th Lecture
2.1 Linear Functions and Lines
the slope of the line through (x, y) and (x, y) x=x is
m= y-y/x-x= rise/run
any point (x, y) on the line through (x, y) with slope m, satisfies y-y/x-x=m
point slope form
(y-y)=m(x-x)
if you plug
October 1st Lecture
2.3 Integer Exponents
x is a real number, m is a positive integer
m*x= x + x + . + x m summands
properties: suppose x, y real numbers m and n positive integers
2.4 Polynomials
a polynomial is a function p of the form p(x)=. n a no
October 5th Lecture
2.5 Rational Functions
Definition: a rational function r has the form r(x)= p(x)/q(x) where p, q are polynomials and
q(x) does not equal zero
Add/Subtract rational functions
Division of Polynomials
Theorem: if p and q are polynomi
October 10th Lecture
Problem: Complete z4 where z=square root of 2/2 all times (1+i)=-1
Fundamental Theorem of Algebra (Lauss)
suppose p is a polynomial of degree n > 1, then there exist complex numbers r, . , r and a
constant c are all real numbers su
October 19th Lecture
Quiz Solutions
The common logarithm: log 10 or log
Note: the common log of an n-digit number is in [n-1, n]
Example: suppose log m = 12.6, log n = 3.2
How many digits does m/n have?
Theorem: if b and y are positive numbers, b does n
October 24th Lecture
4.2 Areas of Simple Regions
the area of a square of side length l or l squared
the area of a rectangle with base b and height h is bh
the area of a parallelogram with base b and height h is bh
the area of a triangle with base b and he
October 31st Lecture
4.4 Approximations with e and natural log (ln)
Remember: ln c = area (1/x, 1, c) = area under graph of y = 1/x between x=1 and x=c
We can approximate ln (1+t) by the area of rectangle t*1=t
if t is close to 0, then ln (1+t)=t
if
MATH 114 FINAL EXAM
December 16, 2013
Your name:
Circle your TAs name:
Sid Kiblawi, Konstantinos Mavrakakis, Michael Mostek, Sowmya Acharya
Bae Jun Park, Fan Zheng, Lalit Jain, Robin Prakash, Ethan Frost
0 Be sure to show your work and explain What you di
M. at ital/4y
MATH 114 - FINAL EXAM
May 13, 2013
Your name:
Circle your TAs name: Rui Wang Sid Kiblawi
0 Be sure to show your work and explain what you did. You. will receive
reduced or zero credit for unsubstantiated answers.
0 No books or calculators. Y
Department of Mathematics, University of Wisconsin-Madison
Math 114 Fall 2014
Review Midterm #1
1. Find the domain of the following. Write your answer in interval notation.
(a) 2x 3
(b)
3
2x 3
(c)
p
|x + 4| + 2
(d)
p
|x + 4| 2
(e)
2x+1
x3
2. Solve. Write
Department of Mathematics, University of Wisconsin-Madison
Math 114 Fall 2014
Worksheet Sections 6.1-6.3
1. For the following functions, sketch the graph and nd the range, amplitude, and period.
(a) g(x) = sin(5x) on the interval [, ]
Solution
The range o
Department of Mathematics, University of Wisconsin-Madison
Math 114 Fall 2014
Worksheet Section 3.1
1. Evaluate the indicated expression. Do not use a calculator.
(a) log2 64
(b) log2
1
16
(c) log8 2
(d) log 100
1
(e) log 100
(f) log
10000
(g) log8 26.3
2
Department of Mathematics, University of Wisconsin-Madison
Math 114 Fall 2014
Worksheet Sections 3.2-3.4
1. Suppose x is such that log6 x = 23.41. Evaluate log6 (x10 ).
2. Suppose log a = 203.4 and log b = 205.4, evaluate
3. Evaluate the given quantities
Department of Mathematics, University of Wisconsin-Madison
Math 114 Fall 2014
Worksheet Sections 3.5-3.7
1. Find a number c such that
(a) ln c = 5
Solution
c = e5
(b) ln c = 3
Solution
c = e3
(c) ln(3c 2) = 5
Solution
3c 2 = e5 3c = e5 + 2 c =
1
e5 + 2
3