MathematicalVocations
ByJaronParke
Jaron Parke
Professor Hathaway
MATH-148
November 21, 2013
Actuary
When graduating with a degree in mathematics, there are many options when it comes to
the career path you will choose. One career that is not well-known,
Chapter 6 Inverse Functions
6.8 Indeterminate Forms and LHospitals Rule
M148 Section 6.8 Indeterminate Forms and LHospitals Rule
Introduction
How to nd limits of these forms
0
0
0
0 , , 0 , , 0 , , 1 ?
M148 Section 6.8 Indeterminate Forms and LHospitals
Chapter 6 Inverse Functions
6.4 Derivatives of Logarithmic Functions
M148 Section 6.4 Derivatives of Logarithmic Functions
Introduction
How to dierentiate ln x?
How to dierentiate loga x?
How to dierentiate ax ?
1
How to integrate x ?
What is logarithmic
Chapter 6 Inverse Functions
6.1 Inverse Functions
M148 Section 6.1 Inverse Functions
Introduction
What is an inverse function?
When does a function have an inverse?
How is the inverse function related to the original function?
How to nd an inverse functio
Chapter 7 Techniques of Integration
7.4 Integration of Rational Functions
by Partial Fractions
M148 7.4 Integration of Rational Functions by Partial Fractions
Introduction
Integrals of the following form:
P(x)
dx
Q(x)
where P(x) and Q(x) are polynomials.
Chapter 7 Techniques of Integration
7.7 Approximate Integration
M148 Section 7.7 Approximate Integration
Introduction
When its dicult or impossible to nd the formula for the
2
2
cos x 2 dx,
antiderivative, such as
1
3
e x dx.
1
M148 Section 7.7 Approximat
Chapter 6 Inverse Functions
6.3 Logarithmic Functions
M148 Section 6.3 Logarithmic Functions
Introduction
What is a logarithmic function?
What does a logarithmic function look like?
How does a logarithmic function operate?
M148 Section 6.3 Logarithmic Fun
Chapter 7 Techniques of Integration
7.8 Improper Integrals
M148 Section 7.8 Improper Integrals
Introduction
Integrals of the following form:
a
b
f (x) dx;
f (x) dx;
and
f (x) dx
b
f (x) dx
a
M148 Section 7.8 Improper Integrals
Improper Integrals: Type I
E
Chapter 7 Techniques of Integration
7.1 Integration by Parts
M148 Section 7.1 Integration by Parts
Introduction
Recall the Product Rule for dierentiation
f (x)g (x)
= f (x)g (x) + f (x)g (x)
M148 Section 7.1 Integration by Parts
Introduction
Recall the Pr
Chapter 6 Inverse Functions
6.2 Exponential Functions and Their Derivatives
M148 Section 6.2 Exponential Functions and Their Derivatives
Introduction
What is an exponential function?
What does an exponential function look like?
How to dierentiate an expon
Chapter 7 Techniques of Integration
7.2 Trigonometric Integrals
M148 Section 7.2 Trigonometric Integrals
Introduction
Integrals of the following forms:
sinm x cosn x dx
secm x tann x dx
sin mx cos nx dx,
sin mx sin nx dx,
cos mx cos nx dx
M148 Section 7.2