MATH 151 Engineering Math I, Spring 2014
JD Kim
Week4 Section 2.6, 2.7, 3.1, 3.2
Section 2.6 Limits at Innity; Horizontal Asymptotes
Denition. Let f be a function dened on some interval (a, ). Then
lim f (x) = L
x
means that the values of f (x) can be mad
MATH 151 Engineering Math I, Spring 2014
JD Kim
Week3 Section 2.2, 2.3, 2.5-2.6, (quantitative) denition of limit, calculation of
limits, limits at innity, continuity.
Section 2.2 The limit of a function
Lets investigate the behavior of the funtion f dene
MATH 151 Engineering Math I, Spring 2014
JD Kim
Week2 Section 1.2, 1.3, 2.2, Dot product, parametrized curves, (qualitative) denition of limit
Section 1.2 The Dot Product
The work done by a constant force F in moving an object through a distant d is
W = F
MATH 151 Engineering Math I, Spring 2014
JD Kim
Week1 Appendix D, Section 1.1 Introduction, Trigonometry review, Two-dimensional
vectors
Domain of a function
Ex1) Find the domain of f (x) =
Ex2) Find the domain of f (x) =
Ex3) Find the domain of f (x) =
x
MATH 151 Engineering Math I, Spring 2014
JD Kim
Week5 Section 3.2, 3.3
Section 3.2 Dierentiation Formulas.
Dierentiation Formulas
1. Constant rule: If f (x) = c, where c is a constant then f (x) = 0.
2. Power rule: If f (x) = xn , then f (x) = n xn1 .
3.
MATH 151 Engineering Math I, Spring 2014
JD Kim
Week7 Section 3.8, 3.9, 3.10
Section 3.8 Higher Derivatives
Denition If y = f (x), then the second derivative of f (x) is the derivative of the
rst derivative. We denote the second derivative as y = (f (x) =
MATH 151 Engineering Math I, Spring 2014
JD Kim
Week6 Section 3.4, 3.5, 3.6, 3.7
Section 3.4 Derivatives of Trigonometric Functions
Two Special limits
1.
sin x
=1
x0 x
lim
2.
cos x 1
=0
x0
x
lim
Ex1) Find the limit
1-1) limx0
sin x
3x
1
1-2) limx0
sin 9x